edit this statistic or download as text // json
Identifier
Values
=>
0=>0 1=>1 00=>0 01=>1 10=>1 11=>2 000=>0 001=>1 010=>1 011=>2 100=>1 101=>1 110=>2 111=>3 0000=>0 0001=>1 0010=>1 0011=>2 0100=>1 0101=>1 0110=>2 0111=>3 1000=>1 1001=>1 1010=>1 1011=>2 1100=>2 1101=>2 1110=>3 1111=>4 00000=>0 00001=>1 00010=>1 00011=>2 00100=>1 00101=>1 00110=>2 00111=>3 01000=>1 01001=>1 01010=>1 01011=>2 01100=>2 01101=>2 01110=>3 01111=>4 10000=>1 10001=>1 10010=>1 10011=>2 10100=>1 10101=>1 10110=>2 10111=>3 11000=>2 11001=>2 11010=>2 11011=>2 11100=>3 11101=>3 11110=>4 11111=>5 000000=>0 000001=>1 000010=>1 000011=>2 000100=>1 000101=>1 000110=>2 000111=>3 001000=>1 001001=>1 001010=>1 001011=>2 001100=>2 001101=>2 001110=>3 001111=>4 010000=>1 010001=>1 010010=>1 010011=>2 010100=>1 010101=>1 010110=>2 010111=>3 011000=>2 011001=>2 011010=>2 011011=>2 011100=>3 011101=>3 011110=>4 011111=>5 100000=>1 100001=>1 100010=>1 100011=>2 100100=>1 100101=>1 100110=>2 100111=>3 101000=>1 101001=>1 101010=>1 101011=>2 101100=>2 101101=>2 101110=>3 101111=>4 110000=>2 110001=>2 110010=>2 110011=>2 110100=>2 110101=>2 110110=>2 110111=>3 111000=>3 111001=>3 111010=>3 111011=>3 111100=>4 111101=>4 111110=>5 111111=>6 0000000=>0 0000001=>1 0000010=>1 0000011=>2 0000100=>1 0000101=>1 0000110=>2 0000111=>3 0001000=>1 0001001=>1 0001010=>1 0001011=>2 0001100=>2 0001101=>2 0001110=>3 0001111=>4 0010000=>1 0010001=>1 0010010=>1 0010011=>2 0010100=>1 0010101=>1 0010110=>2 0010111=>3 0011000=>2 0011001=>2 0011010=>2 0011011=>2 0011100=>3 0011101=>3 0011110=>4 0011111=>5 0100000=>1 0100001=>1 0100010=>1 0100011=>2 0100100=>1 0100101=>1 0100110=>2 0100111=>3 0101000=>1 0101001=>1 0101010=>1 0101011=>2 0101100=>2 0101101=>2 0101110=>3 0101111=>4 0110000=>2 0110001=>2 0110010=>2 0110011=>2 0110100=>2 0110101=>2 0110110=>2 0110111=>3 0111000=>3 0111001=>3 0111010=>3 0111011=>3 0111100=>4 0111101=>4 0111110=>5 0111111=>6 1000000=>1 1000001=>1 1000010=>1 1000011=>2 1000100=>1 1000101=>1 1000110=>2 1000111=>3 1001000=>1 1001001=>1 1001010=>1 1001011=>2 1001100=>2 1001101=>2 1001110=>3 1001111=>4 1010000=>1 1010001=>1 1010010=>1 1010011=>2 1010100=>1 1010101=>1 1010110=>2 1010111=>3 1011000=>2 1011001=>2 1011010=>2 1011011=>2 1011100=>3 1011101=>3 1011110=>4 1011111=>5 1100000=>2 1100001=>2 1100010=>2 1100011=>2 1100100=>2 1100101=>2 1100110=>2 1100111=>3 1101000=>2 1101001=>2 1101010=>2 1101011=>2 1101100=>2 1101101=>2 1101110=>3 1101111=>4 1110000=>3 1110001=>3 1110010=>3 1110011=>3 1110100=>3 1110101=>3 1110110=>3 1110111=>3 1111000=>4 1111001=>4 1111010=>4 1111011=>4 1111100=>5 1111101=>5 1111110=>6 1111111=>7 00000000=>0 00000001=>1 00000010=>1 00000011=>2 00000100=>1 00000101=>1 00000110=>2 00000111=>3 00001000=>1 00001001=>1 00001010=>1 00001011=>2 00001100=>2 00001101=>2 00001110=>3 00001111=>4 00010000=>1 00010001=>1 00010010=>1 00010011=>2 00010100=>1 00010101=>1 00010110=>2 00010111=>3 00011000=>2 00011001=>2 00011010=>2 00011011=>2 00011100=>3 00011101=>3 00011110=>4 00011111=>5 00100000=>1 00100001=>1 00100010=>1 00100011=>2 00100100=>1 00100101=>1 00100110=>2 00100111=>3 00101000=>1 00101001=>1 00101010=>1 00101011=>2 00101100=>2 00101101=>2 00101110=>3 00101111=>4 00110000=>2 00110001=>2 00110010=>2 00110011=>2 00110100=>2 00110101=>2 00110110=>2 00110111=>3 00111000=>3 00111001=>3 00111010=>3 00111011=>3 00111100=>4 00111101=>4 00111110=>5 00111111=>6 01000000=>1 01000001=>1 01000010=>1 01000011=>2 01000100=>1 01000101=>1 01000110=>2 01000111=>3 01001000=>1 01001001=>1 01001010=>1 01001011=>2 01001100=>2 01001101=>2 01001110=>3 01001111=>4 01010000=>1 01010001=>1 01010010=>1 01010011=>2 01010100=>1 01010101=>1 01010110=>2 01010111=>3 01011000=>2 01011001=>2 01011010=>2 01011011=>2 01011100=>3 01011101=>3 01011110=>4 01011111=>5 01100000=>2 01100001=>2 01100010=>2 01100011=>2 01100100=>2 01100101=>2 01100110=>2 01100111=>3 01101000=>2 01101001=>2 01101010=>2 01101011=>2 01101100=>2 01101101=>2 01101110=>3 01101111=>4 01110000=>3 01110001=>3 01110010=>3 01110011=>3 01110100=>3 01110101=>3 01110110=>3 01110111=>3 01111000=>4 01111001=>4 01111010=>4 01111011=>4 01111100=>5 01111101=>5 01111110=>6 01111111=>7 10000000=>1 10000001=>1 10000010=>1 10000011=>2 10000100=>1 10000101=>1 10000110=>2 10000111=>3 10001000=>1 10001001=>1 10001010=>1 10001011=>2 10001100=>2 10001101=>2 10001110=>3 10001111=>4 10010000=>1 10010001=>1 10010010=>1 10010011=>2 10010100=>1 10010101=>1 10010110=>2 10010111=>3 10011000=>2 10011001=>2 10011010=>2 10011011=>2 10011100=>3 10011101=>3 10011110=>4 10011111=>5 10100000=>1 10100001=>1 10100010=>1 10100011=>2 10100100=>1 10100101=>1 10100110=>2 10100111=>3 10101000=>1 10101001=>1 10101010=>1 10101011=>2 10101100=>2 10101101=>2 10101110=>3 10101111=>4 10110000=>2 10110001=>2 10110010=>2 10110011=>2 10110100=>2 10110101=>2 10110110=>2 10110111=>3 10111000=>3 10111001=>3 10111010=>3 10111011=>3 10111100=>4 10111101=>4 10111110=>5 10111111=>6 11000000=>2 11000001=>2 11000010=>2 11000011=>2 11000100=>2 11000101=>2 11000110=>2 11000111=>3 11001000=>2 11001001=>2 11001010=>2 11001011=>2 11001100=>2 11001101=>2 11001110=>3 11001111=>4 11010000=>2 11010001=>2 11010010=>2 11010011=>2 11010100=>2 11010101=>2 11010110=>2 11010111=>3 11011000=>2 11011001=>2 11011010=>2 11011011=>2 11011100=>3 11011101=>3 11011110=>4 11011111=>5 11100000=>3 11100001=>3 11100010=>3 11100011=>3 11100100=>3 11100101=>3 11100110=>3 11100111=>3 11101000=>3 11101001=>3 11101010=>3 11101011=>3 11101100=>3 11101101=>3 11101110=>3 11101111=>4 11110000=>4 11110001=>4 11110010=>4 11110011=>4 11110100=>4 11110101=>4 11110110=>4 11110111=>4 11111000=>5 11111001=>5 11111010=>5 11111011=>5 11111100=>6 11111101=>6 11111110=>7 11111111=>8 000000000=>0 000000001=>1 000000010=>1 000000011=>2 000000100=>1 000000101=>1 000000110=>2 000000111=>3 000001000=>1 000001001=>1 000001010=>1 000001011=>2 000001100=>2 000001101=>2 000001110=>3 000001111=>4 000010000=>1 000010001=>1 000010010=>1 000010011=>2 000010100=>1 000010101=>1 000010110=>2 000010111=>3 000011000=>2 000011001=>2 000011010=>2 000011011=>2 000011100=>3 000011101=>3 000011110=>4 000011111=>5 000100000=>1 000100001=>1 000100010=>1 000100011=>2 000100100=>1 000100101=>1 000100110=>2 000100111=>3 000101000=>1 000101001=>1 000101010=>1 000101011=>2 000101100=>2 000101101=>2 000101110=>3 000101111=>4 000110000=>2 000110001=>2 000110010=>2 000110011=>2 000110100=>2 000110101=>2 000110110=>2 000110111=>3 000111000=>3 000111001=>3 000111010=>3 000111011=>3 000111100=>4 000111101=>4 000111110=>5 000111111=>6 001000000=>1 001000001=>1 001000010=>1 001000011=>2 001000100=>1 001000101=>1 001000110=>2 001000111=>3 001001000=>1 001001001=>1 001001010=>1 001001011=>2 001001100=>2 001001101=>2 001001110=>3 001001111=>4 001010000=>1 001010001=>1 001010010=>1 001010011=>2 001010100=>1 001010101=>1 001010110=>2 001010111=>3 001011000=>2 001011001=>2 001011010=>2 001011011=>2 001011100=>3 001011101=>3 001011110=>4 001011111=>5 001100000=>2 001100001=>2 001100010=>2 001100011=>2 001100100=>2 001100101=>2 001100110=>2 001100111=>3 001101000=>2 001101001=>2 001101010=>2 001101011=>2 001101100=>2 001101101=>2 001101110=>3 001101111=>4 001110000=>3 001110001=>3 001110010=>3 001110011=>3 001110100=>3 001110101=>3 001110110=>3 001110111=>3 001111000=>4 001111001=>4 001111010=>4 001111011=>4 001111100=>5 001111101=>5 001111110=>6 001111111=>7 010000000=>1 010000001=>1 010000010=>1 010000011=>2 010000100=>1 010000101=>1 010000110=>2 010000111=>3 010001000=>1 010001001=>1 010001010=>1 010001011=>2 010001100=>2 010001101=>2 010001110=>3 010001111=>4 010010000=>1 010010001=>1 010010010=>1 010010011=>2 010010100=>1 010010101=>1 010010110=>2 010010111=>3 010011000=>2 010011001=>2 010011010=>2 010011011=>2 010011100=>3 010011101=>3 010011110=>4 010011111=>5 010100000=>1 010100001=>1 010100010=>1 010100011=>2 010100100=>1 010100101=>1 010100110=>2 010100111=>3 010101000=>1 010101001=>1 010101010=>1 010101011=>2 010101100=>2 010101101=>2 010101110=>3 010101111=>4 010110000=>2 010110001=>2 010110010=>2 010110011=>2 010110100=>2 010110101=>2 010110110=>2 010110111=>3 010111000=>3 010111001=>3 010111010=>3 010111011=>3 010111100=>4 010111101=>4 010111110=>5 010111111=>6 011000000=>2 011000001=>2 011000010=>2 011000011=>2 011000100=>2 011000101=>2 011000110=>2 011000111=>3 011001000=>2 011001001=>2 011001010=>2 011001011=>2 011001100=>2 011001101=>2 011001110=>3 011001111=>4 011010000=>2 011010001=>2 011010010=>2 011010011=>2 011010100=>2 011010101=>2 011010110=>2 011010111=>3 011011000=>2 011011001=>2 011011010=>2 011011011=>2 011011100=>3 011011101=>3 011011110=>4 011011111=>5 011100000=>3 011100001=>3 011100010=>3 011100011=>3 011100100=>3 011100101=>3 011100110=>3 011100111=>3 011101000=>3 011101001=>3 011101010=>3 011101011=>3 011101100=>3 011101101=>3 011101110=>3 011101111=>4 011110000=>4 011110001=>4 011110010=>4 011110011=>4 011110100=>4 011110101=>4 011110110=>4 011110111=>4 011111000=>5 011111001=>5 011111010=>5 011111011=>5 011111100=>6 011111101=>6 011111110=>7 011111111=>8 100000000=>1 100000001=>1 100000010=>1 100000011=>2 100000100=>1 100000101=>1 100000110=>2 100000111=>3 100001000=>1 100001001=>1 100001010=>1 100001011=>2 100001100=>2 100001101=>2 100001110=>3 100001111=>4 100010000=>1 100010001=>1 100010010=>1 100010011=>2 100010100=>1 100010101=>1 100010110=>2 100010111=>3 100011000=>2 100011001=>2 100011010=>2 100011011=>2 100011100=>3 100011101=>3 100011110=>4 100011111=>5 100100000=>1 100100001=>1 100100010=>1 100100011=>2 100100100=>1 100100101=>1 100100110=>2 100100111=>3 100101000=>1 100101001=>1 100101010=>1 100101011=>2 100101100=>2 100101101=>2 100101110=>3 100101111=>4 100110000=>2 100110001=>2 100110010=>2 100110011=>2 100110100=>2 100110101=>2 100110110=>2 100110111=>3 100111000=>3 100111001=>3 100111010=>3 100111011=>3 100111100=>4 100111101=>4 100111110=>5 100111111=>6 101000000=>1 101000001=>1 101000010=>1 101000011=>2 101000100=>1 101000101=>1 101000110=>2 101000111=>3 101001000=>1 101001001=>1 101001010=>1 101001011=>2 101001100=>2 101001101=>2 101001110=>3 101001111=>4 101010000=>1 101010001=>1 101010010=>1 101010011=>2 101010100=>1 101010101=>1 101010110=>2 101010111=>3 101011000=>2 101011001=>2 101011010=>2 101011011=>2 101011100=>3 101011101=>3 101011110=>4 101011111=>5 101100000=>2 101100001=>2 101100010=>2 101100011=>2 101100100=>2 101100101=>2 101100110=>2 101100111=>3 101101000=>2 101101001=>2 101101010=>2 101101011=>2 101101100=>2 101101101=>2 101101110=>3 101101111=>4 101110000=>3 101110001=>3 101110010=>3 101110011=>3 101110100=>3 101110101=>3 101110110=>3 101110111=>3 101111000=>4 101111001=>4 101111010=>4 101111011=>4 101111100=>5 101111101=>5 101111110=>6 101111111=>7 110000000=>2 110000001=>2 110000010=>2 110000011=>2 110000100=>2 110000101=>2 110000110=>2 110000111=>3 110001000=>2 110001001=>2 110001010=>2 110001011=>2 110001100=>2 110001101=>2 110001110=>3 110001111=>4 110010000=>2 110010001=>2 110010010=>2 110010011=>2 110010100=>2 110010101=>2 110010110=>2 110010111=>3 110011000=>2 110011001=>2 110011010=>2 110011011=>2 110011100=>3 110011101=>3 110011110=>4 110011111=>5 110100000=>2 110100001=>2 110100010=>2 110100011=>2 110100100=>2 110100101=>2 110100110=>2 110100111=>3 110101000=>2 110101001=>2 110101010=>2 110101011=>2 110101100=>2 110101101=>2 110101110=>3 110101111=>4 110110000=>2 110110001=>2 110110010=>2 110110011=>2 110110100=>2 110110101=>2 110110110=>2 110110111=>3 110111000=>3 110111001=>3 110111010=>3 110111011=>3 110111100=>4 110111101=>4 110111110=>5 110111111=>6 111000000=>3 111000001=>3 111000010=>3 111000011=>3 111000100=>3 111000101=>3 111000110=>3 111000111=>3 111001000=>3 111001001=>3 111001010=>3 111001011=>3 111001100=>3 111001101=>3 111001110=>3 111001111=>4 111010000=>3 111010001=>3 111010010=>3 111010011=>3 111010100=>3 111010101=>3 111010110=>3 111010111=>3 111011000=>3 111011001=>3 111011010=>3 111011011=>3 111011100=>3 111011101=>3 111011110=>4 111011111=>5 111100000=>4 111100001=>4 111100010=>4 111100011=>4 111100100=>4 111100101=>4 111100110=>4 111100111=>4 111101000=>4 111101001=>4 111101010=>4 111101011=>4 111101100=>4 111101101=>4 111101110=>4 111101111=>4 111110000=>5 111110001=>5 111110010=>5 111110011=>5 111110100=>5 111110101=>5 111110110=>5 111110111=>5 111111000=>6 111111001=>6 111111010=>6 111111011=>6 111111100=>7 111111101=>7 111111110=>8 111111111=>9 1010101010=>1 1010101100=>2 1010110010=>2 1010110100=>2 1010111000=>3 1011001010=>2 1011001100=>2 1011010010=>2 1011010100=>2 1011011000=>2 1011100010=>3 1011100100=>3 1011101000=>3 1011110000=>4 1100101010=>2 1100101100=>2 1100110010=>2 1100110100=>2 1100111000=>3 1101001010=>2 1101001100=>2 1101010010=>2 1101010100=>2 1101011000=>2 1101100010=>2 1101100100=>2 1101101000=>2 1101110000=>3 1110001010=>3 1110001100=>3 1110010010=>3 1110010100=>3 1110011000=>3 1110100010=>3 1110100100=>3 1110101000=>3 1110110000=>3 1111000010=>4 1111000100=>4 1111001000=>4 1111010000=>4 1111100000=>5 1111111110=>9 1111111101=>8 1111000001=>4 1110111110=>5 1110100001=>3 1110011110=>4 1110010001=>3 1110001001=>3 1110000101=>3 1101111110=>6 1101100001=>2 1101010001=>2 1101001110=>3 1101001001=>2 1101000101=>2 1100110001=>2 1100101001=>2 1100100110=>2 1100100101=>2 1100011001=>2 1100010101=>2 1100010010=>2 1100001000=>2 1011111110=>7 1011111101=>6 1011100001=>3 1011010001=>2 1011001001=>2 1011000101=>2 1010111110=>5 1010110001=>2 1010101001=>1 1010100110=>2 1010100101=>1 1010011010=>2 1010011001=>2 1010010110=>2 1010010101=>1 1010001110=>3 1001111110=>6 1001111000=>4 1001110100=>3 1001110001=>3 1001101100=>2 1001101010=>2 1001101001=>2 1001100110=>2 1001100101=>2 1001011110=>4 1001011010=>2 1001011001=>2 1001010110=>2 1001010101=>1 1001001110=>3 1000111110=>5 1000111100=>4 1000111010=>3 1000110110=>2 1000101110=>3 1000011110=>4 1000010110=>2 1000001110=>3 1000001010=>1 1000000110=>2 1000000100=>1 1000000010=>1 1000000000=>1 0111111111=>9 0111111101=>7 0111111001=>6 0111110001=>5 0111100001=>4 0111000001=>3 0110000001=>2 0100000001=>1 0000000001=>1 0111111011=>6 0111110101=>5 0111101001=>4 0111010001=>3 0110100001=>2 0101000001=>1 0010000001=>1 0101010101=>1 0101010011=>2 0101001101=>2 0101001011=>2 0101000111=>3 0100110101=>2 0100110011=>2 0100101101=>2 0100101011=>2 0100100111=>3 0100011101=>3 0100011011=>2 0100010111=>3 0100001111=>4 0011010101=>2 0011010011=>2 0011001101=>2 0011001011=>2 0011000111=>3 0010110101=>2 0010110011=>2 0010101101=>2 0010101011=>2 0010100111=>3 0010011101=>3 0010011011=>2 0010010111=>3 0010001111=>4 0001110101=>3 0001110011=>3 0001101101=>2 0001101011=>2 0001100111=>3 0001011101=>3 0001011011=>2 0001010111=>3 0001001111=>4 0000111101=>4 0000111011=>3 0000110111=>3 0000101111=>4 0000011111=>5 0000000000=>0 0000000110=>2 0000011000=>2 0000011110=>4 0000010010=>1 0001100000=>2 0001100110=>2 0001111000=>4 0001111110=>6 0001110010=>3 0001001000=>1 0001001110=>3 0001000010=>1 0001011010=>2 0100000010=>1 0010101010=>1 0010101000=>1 0010101100=>2 0010100100=>1 0010010100=>1 0001010100=>1 0010101110=>3 0010100000=>1 0010111100=>4 0010000100=>1 0011110100=>4 0000010100=>1 0111010100=>3 0000000010=>1 0000001110=>3 0000111110=>5 0000000100=>1 0000001010=>1 0000010110=>2 0000101110=>3 0001011110=>4 0100000000=>1 0100000011=>2 0100000111=>3 0100011111=>5 0100111111=>6 0101111111=>7 0100000101=>1 0100001011=>2 0100101111=>4 0101011111=>5 0110111111=>6 0101010110=>2 0101011001=>2 0101011010=>2 0101011100=>3 0101100101=>2 0101100110=>2 0101101001=>2 0101101010=>2 0101101100=>2 0101110001=>3 0101110010=>3 0101110100=>3 0101111000=>4 0110010101=>2 0110010110=>2 0110011001=>2 0110011010=>2 0110011100=>3 0110100101=>2 0110100110=>2 0110101001=>2 0110101010=>2 0110101100=>2 0110110001=>2 0110110010=>2 0110110100=>2 0110111000=>3 0111000101=>3 0111000110=>3 0111001001=>3 0111001010=>3 0111001100=>3 0111010010=>3 0111011000=>3 0111100010=>4 0111100100=>4 0111101000=>4 0111110000=>5 0100000100=>1 0011100110=>3 0011101010=>3 0011101100=>3 0001101110=>3 0010110110=>2 0011110010=>4 0001110110=>3 0100111010=>3 0010111010=>3 0011111000=>5 0001111010=>4 0100111100=>4 0001111100=>5 0000000101=>1 0000001101=>2 0000011101=>3 0001111101=>5 0011111101=>6 0000001001=>1 0000010101=>1 0000101101=>2 0010111101=>4 0101111101=>5 0010110001=>2 0001100001=>2 0001000001=>1 0000111111=>6 0001110100=>3 0001101100=>2 0010011100=>3 0001011100=>3 0000111100=>4 0001101010=>2 0010011010=>2 0000111010=>3 0010100110=>2 0010010110=>2 0001010110=>2 0000110110=>2 0010001110=>3 0001101001=>2 0000110001=>2 0000010001=>1 0000001100=>2 0000011001=>2 0000110011=>2 0000110100=>2 0000000011=>2 0000011011=>2 0001101111=>4 0000110101=>2 0010000010=>1 0001000011=>2 0010011110=>4 0001010000=>1 0001000100=>1 0001010101=>1 0001001011=>2 0001100011=>2 0001110111=>3 0010000000=>1 0000000111=>3 0000001111=>4 0001111111=>7 0000001011=>2 0000010111=>3 0001011111=>5 0001111001=>4 0000011010=>2 0000101010=>1 0000100101=>1 0010010001=>1 0010000101=>1 0010010101=>1 0010010011=>2 0000101011=>2 0001000111=>3 0000100111=>3 0010010010=>1 0001001010=>1 0001001001=>1 0001000101=>1 0000100011=>2 0000100100=>1 0000100010=>1 0010110000=>2 0000011100=>3 0000001000=>1 0000101100=>2 0010101111=>4 0000101000=>1 0010001000=>1 0001001100=>2 0001000110=>2 0001100100=>2 0001100010=>2 0000100110=>2 0000110010=>2 0010010000=>1 0001010010=>1 0001000000=>1 0001011001=>2 0001100101=>2 0001110001=>3 0010011001=>2 0010100101=>1 0010101001=>1 0010011111=>5 0000111001=>3 0010001101=>2 0001001101=>2 0001010001=>1 0001010011=>2 0001111011=>4 0010011000=>2 0001011000=>2 0000100000=>1 0010001011=>2 0010000111=>3 0000010011=>2 0010001100=>2 0010000110=>2 0000110000=>2 0000100001=>1 0010100011=>2 0010100001=>1 0000111000=>3 0001101000=>2 0000010000=>1 0000101001=>1 0010100010=>1 0010001001=>1 0010000011=>2 0010001010=>1 0001110000=>3 10000000000=>1 10000000010=>1 10000000110=>2 10000001110=>3 10000011110=>4 10000111110=>5 10001111110=>6 10011111110=>7 10111111110=>8 11111111110=>10 10000000100=>1 10000001010=>1 10000010110=>2 10000101110=>3 10001011110=>4 10010111110=>5 10101111110=>6 11011111110=>7 10000010000=>1 10000100010=>1 10001000010=>1 10000100100=>1 10001001010=>1 10001000100=>1 10000101000=>1 10010001010=>1 10001010010=>1 10010000100=>1 10001001000=>1 10010010010=>1 10001010100=>1 10010101010=>1 10010001000=>1 10100010010=>1 10010100010=>1 10010010100=>1 10100101010=>1 01111111111=>10 01111111101=>8 01111111001=>7 01111110001=>6 01111100001=>5 01111000001=>4 01110000001=>3 01100000001=>2 01000000001=>1 00000000001=>1 00000000010=>1 10101010101=>1 10101010010=>1 10101001001=>1 10101001010=>1 10101000100=>1 10100100101=>1 10100100010=>1 10100101001=>1 10100100100=>1 10100010001=>1 10100010100=>1 10100001000=>1 10010010101=>1 10010001001=>1 10010100101=>1 10010101001=>1 10010100100=>1 10010010001=>1 10001000101=>1 10001001001=>1 10001010001=>1 10000100001=>1 01001010101=>1 01001010010=>1 01001001001=>1 01001001010=>1 01001000100=>1 01000100101=>1 01000100010=>1 01000101001=>1 01000101010=>1 01000100100=>1 01000010001=>1 01000010010=>1 01000010100=>1 01000001000=>1 01010010101=>1 01010010010=>1 01010001001=>1 01010001010=>1 01010000100=>1 01010100101=>1 01010100010=>1 01010101001=>1 01010101010=>1 01010100100=>1 01010010001=>1 01010010100=>1 01010001000=>1 01001000101=>1 01001000010=>1 01001010001=>1 01001010100=>1 01001001000=>1 01000100001=>1 01000101000=>1 01000010000=>1 00100010101=>1 00100010010=>1 00100001001=>1 00100001010=>1 00100000100=>1 00100100101=>1 00100100010=>1 00100101001=>1 00100101010=>1 00100100100=>1 00100010001=>1 00100010100=>1 00100001000=>1 00101000101=>1 00101000010=>1 00101001001=>1 00101001010=>1 00101000100=>1 00101010001=>1 00101010010=>1 00101010100=>1 00101001000=>1 00100100001=>1 00100101000=>1 00100010000=>1 00010000101=>1 00010000010=>1 00010001001=>1 00010001010=>1 00010000100=>1 00010010001=>1 00010010010=>1 00010010100=>1 00010001000=>1 00010100001=>1 00010100010=>1 00010100100=>1 00010101000=>1 00010010000=>1 00001000001=>1 00001000010=>1 00001000100=>1 00001001000=>1 00001010000=>1 00000100000=>1 01000000000=>1 01000000011=>2 01000000111=>3 01000001111=>4 01000011111=>5 01000111111=>6 01001111111=>7 01011111111=>8 00000000101=>1 00000001101=>2 00000011101=>3 00000111101=>4 00001111101=>5 00011111101=>6 00111111101=>7 11111111101=>9 101010101010=>1 101010101100=>2 101010110010=>2 101010110100=>2 101010111000=>3 101011001010=>2 101011001100=>2 101011010010=>2 101011010100=>2 101011011000=>2 101011100010=>3 101011100100=>3 101011101000=>3 101011110000=>4 101100101010=>2 101100101100=>2 101100110010=>2 101100110100=>2 101100111000=>3 101101001010=>2 101101001100=>2 101101010010=>2 101101010100=>2 101101011000=>2 101101100010=>2 101101100100=>2 101101101000=>2 101101110000=>3 101110001010=>3 101110001100=>3 101110010010=>3 101110010100=>3 101110011000=>3 101110100010=>3 101110100100=>3 101110101000=>3 101110110000=>3 101111000010=>4 101111000100=>4 101111001000=>4 101111010000=>4 101111100000=>5 110010101010=>2 110010101100=>2 110010110010=>2 110010110100=>2 110010111000=>3 110011001010=>2 110011001100=>2 110011010010=>2 110011010100=>2 110011011000=>2 110011100010=>3 110011100100=>3 110011101000=>3 110011110000=>4 110100101010=>2 110100101100=>2 110100110010=>2 110100110100=>2 110100111000=>3 110101001010=>2 110101001100=>2 110101010010=>2 110101010100=>2 110101011000=>2 110101100010=>2 110101100100=>2 110101101000=>2 110101110000=>3 110110001010=>2 110110001100=>2 110110010010=>2 110110010100=>2 110110011000=>2 110110100010=>2 110110100100=>2 110110101000=>2 110110110000=>2 110111000010=>3 110111000100=>3 110111001000=>3 110111010000=>3 110111100000=>4 111000101010=>3 111000101100=>3 111000110010=>3 111000110100=>3 111000111000=>3 111001001010=>3 111001001100=>3 111001010010=>3 111001010100=>3 111001011000=>3 111001100010=>3 111001100100=>3 111001101000=>3 111001110000=>3 111010001010=>3 111010001100=>3 111010010010=>3 111010010100=>3 111010011000=>3 111010100010=>3 111010100100=>3 111010101000=>3 111010110000=>3 111011000010=>3 111011000100=>3 111011001000=>3 111011010000=>3 111011100000=>3 111100001010=>4 111100001100=>4 111100010010=>4 111100010100=>4 111100011000=>4 111100100010=>4 111100100100=>4 111100101000=>4 111100110000=>4 111101000010=>4 111101000100=>4 111101001000=>4 111101010000=>4 111101100000=>4 111110000010=>5 111110000100=>5 111110001000=>5 111110010000=>5 111110100000=>5 111111000000=>6 100001111100=>5 010101010101=>1 010101010011=>2 010101001101=>2 010101001011=>2 010101000111=>3 010100110101=>2 010100110011=>2 010100101101=>2 010100101011=>2 010100100111=>3 010100011101=>3 010100011011=>2 010100010111=>3 010100001111=>4 010011010101=>2 010011010011=>2 010011001101=>2 010011001011=>2 010011000111=>3 010010110101=>2 010010110011=>2 010010101101=>2 010010101011=>2 010010100111=>3 010010011101=>3 010010011011=>2 010010010111=>3 010010001111=>4 010001110101=>3 010001110011=>3 010001101101=>2 010001101011=>2 010001100111=>3 010001011101=>3 010001011011=>2 010001010111=>3 010001001111=>4 010000111101=>4 010000111011=>3 010000110111=>3 010000101111=>4 010000011111=>5 001101010101=>2 001101010011=>2 001101001101=>2 001101001011=>2 001101000111=>3 001100110101=>2 001100110011=>2 001100101101=>2 001100101011=>2 001100100111=>3 001100011101=>3 001100011011=>2 001100010111=>3 001100001111=>4 001011010101=>2 001011010011=>2 001011001101=>2 001011001011=>2 001011000111=>3 001010110101=>2 001010110011=>2 001010101101=>2 001010101011=>2 001010100111=>3 001010011101=>3 001010011011=>2 001010010111=>3 001010001111=>4 001001110101=>3 001001110011=>3 001001101101=>2 001001101011=>2 001001100111=>3 001001011101=>3 001001011011=>2 001001010111=>3 001001001111=>4 001000111101=>4 001000111011=>3 001000110111=>3 001000101111=>4 001000011111=>5 000111010101=>3 000111010011=>3 000111001101=>3 000111001011=>3 000111000111=>3 000110110101=>2 000110110011=>2 000110101101=>2 000110101011=>2 000110100111=>3 000110011101=>3 000110011011=>2 000110010111=>3 000110001111=>4 000101110101=>3 000101110011=>3 000101101101=>2 000101101011=>2 000101100111=>3 000101011101=>3 000101011011=>2 000101010111=>3 000101001111=>4 000100111101=>4 000100111011=>3 000100110111=>3 000100101111=>4 000100011111=>5 000011110101=>4 000011110011=>4 000011101101=>3 000011101011=>3 000011100111=>3 000011011101=>3 000011011011=>2 000011010111=>3 000011001111=>4 000010111101=>4 000010111011=>3 000010110111=>3 000010101111=>4 000010011111=>5 000001111101=>5 000001111011=>4 000001110111=>3 000001101111=>4 000001011111=>5 000000111111=>6 111110000001=>5 111001100001=>3 111000011001=>3 111000110001=>3 111000100101=>3 111011000001=>3 111010010001=>3 111010000101=>3 100111100001=>4 100110011001=>2 100110110001=>2 100110100101=>2 101101100001=>2 101100011001=>2 101100110001=>2 101100100101=>2 101111000001=>4 101110010001=>3 101110000101=>3 101001011001=>2 101001110001=>3 101001100101=>2 101011010001=>2 101011000101=>2 101010010101=>1 000001111110=>6 000111100110=>4 000111111000=>6 000111110010=>5 000111001110=>3 000111011010=>3 000101101110=>3 000101111010=>4 011001100110=>2 011001111000=>4 011001110010=>3 011001011010=>2 011110000110=>4 011110011000=>4 011110010010=>4 011111100000=>6 011111001000=>5 011111000010=>5 011100100110=>3 011100111000=>3 011100110010=>3 011100011010=>3 011101101000=>3 011101100010=>3 011101001010=>3 010011111000=>5 010011110010=>4 010011011010=>2 010001111010=>4 010110100110=>2 010110111000=>3 010110110010=>2 010110011010=>2 010111101000=>4 010111100010=>4 010111001010=>3 010101101010=>2 010101010110=>2 010101011001=>2 010101011010=>2 010101011100=>3 010101100101=>2 010101100110=>2 010101101001=>2 010101101100=>2 010101110001=>3 010101110010=>3 010101110100=>3 010101111000=>4 010110010101=>2 010110010110=>2 010110011001=>2 010110011100=>3 010110100101=>2 010110101001=>2 010110101010=>2 010110101100=>2 010110110001=>2 010110110100=>2 010111000101=>3 010111000110=>3 010111001001=>3 010111001100=>3 010111010001=>3 010111010010=>3 010111010100=>3 010111011000=>3 010111100001=>4 010111100100=>4 010111110000=>5 011001010101=>2 011001010110=>2 011001011001=>2 011001011100=>3 011001100101=>2 011001101001=>2 011001101010=>2 011001101100=>2 011001110001=>3 011001110100=>3 011010010101=>2 011010010110=>2 011010011001=>2 011010011010=>2 011010011100=>3 011010100101=>2 011010100110=>2 011010101001=>2 011010101010=>2 011010101100=>2 011010110001=>2 011010110010=>2 011010110100=>2 011010111000=>3 011011000101=>2 011011000110=>2 011011001001=>2 011011001010=>2 011011001100=>2 011011010001=>2 011011010010=>2 011011010100=>2 011011011000=>2 011011100001=>3 011011100010=>3 011011100100=>3 011011101000=>3 011011110000=>4 011100010101=>3 011100010110=>3 011100011001=>3 011100011100=>3 011100100101=>3 011100101001=>3 011100101010=>3 011100101100=>3 011100110001=>3 011100110100=>3 011101000101=>3 011101000110=>3 011101001001=>3 011101001100=>3 011101010001=>3 011101010010=>3 011101010100=>3 011101011000=>3 011101100001=>3 011101100100=>3 011101110000=>3 011110000101=>4 011110001001=>4 011110001010=>4 011110001100=>4 011110010001=>4 011110010100=>4 011110100001=>4 011110100010=>4 011110100100=>4 011110101000=>4 011110110000=>4 011111000001=>5 011111000100=>5 011111010000=>5 001111000110=>4 001111001010=>4 100111001100=>3 001111001100=>4 001011010110=>2 001111010010=>4 100111010100=>3 001111010100=>4 000111010110=>3 001011011010=>2 100111011000=>3 001111011000=>4 100011011100=>3 010011011100=>3 001011011100=>3 000111011100=>3 000011011110=>4 001101100110=>2 001101101010=>2 100101101100=>2 001101101100=>2 001011100110=>3 001111100010=>5 100111100100=>4 001111100100=>5 010011101010=>3 001011101010=>3 100111101000=>4 001111101000=>5 000111101010=>4 100011101100=>3 010011101100=>3 001011101100=>3 000111101100=>4 000011101110=>3 101001110100=>3 001001110110=>3 001101110010=>3 100101110100=>3 001101110100=>3 000101110110=>3 001011110010=>4 100111110000=>5 001111110000=>6 100011110100=>4 010011110100=>4 001011110100=>4 000111110100=>5 000011110110=>4 110001111000=>4 101001111000=>4 001001111010=>4 100101111000=>4 001101111000=>4 100011111000=>5 001011111000=>5 000011111010=>5 010001111100=>5 001001111100=>5 000101111100=>5 000011111100=>6 100101010101=>1 100101011001=>2 100101100101=>2 100101101001=>2 100101110001=>3 100110010101=>2 100110101001=>2 100111000101=>3 100111001001=>3 100111010001=>3 101001010101=>1 101001101001=>2 101010011001=>2 101010100101=>1 101010101001=>1 101010110001=>2 101011001001=>2 101011100001=>3 101100010101=>2 101100101001=>2 101101000101=>2 101101001001=>2 101101010001=>2 101110001001=>3 101110100001=>3 110001010101=>2 110001011001=>2 110001100101=>2 110001101001=>2 110001110001=>3 110010010101=>2 110010011001=>2 110010100101=>2 110010101001=>2 110010110001=>2 110011000101=>2 110011001001=>2 110011010001=>2 110011100001=>3 110100010101=>2 110100011001=>2 110100100101=>2 110100101001=>2 110100110001=>2 110101000101=>2 110101001001=>2 110101010001=>2 110101100001=>2 110110000101=>2 110110001001=>2 110110010001=>2 110110100001=>2 110111000001=>3 111000010101=>3 111000101001=>3 111001000101=>3 111001001001=>3 111001010001=>3 111010001001=>3 111010100001=>3 111100000101=>4 111100001001=>4 111100010001=>4 111100100001=>4 111101000001=>4 10110111100000=>4 10111011010000=>3 10111011100000=>3 10111100110000=>4 10111101001000=>4 10111101010000=>4 10111101100000=>4 10111110000100=>5 10111110001000=>5 10111110010000=>5 10111110100000=>5 10111111000000=>6 11001111100000=>5 11011110000010=>4 11101101000010=>3 11101110000010=>3 11110011000010=>4 11110100100010=>4 11110101000010=>4 11110110000010=>4 11111000001100=>5 11111000010010=>5 11111000100010=>5 11111001000010=>5 11111010000010=>5 11111100000010=>6 1011110111000000=>4 1011111010100000=>5 1011111011000000=>5 1011111100010000=>6 1011111100100000=>6 1011111101000000=>6 1011111110000000=>7 1111011100000010=>4 1111101010000010=>5 1111101100000010=>5 1111110001000010=>6 1111110010000010=>6 1111110100000010=>6 1111111000000010=>7 111111110000000010=>8 101111111100000000=>8 111111101000000010=>7 101111111010000000=>7 111111100100000010=>7 111111011000000010=>6 101111111001000000=>7 101111110110000000=>6 11111111100000000010=>9 10111111111000000000=>9 11111111010000000010=>8 10111111110100000000=>8 1111111111000000000010=>10 1011111111110000000000=>10
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Description
The length of the longest run of ones in a binary word.
References
[1] Triangular array read by rows: T(n,k) = number of binary vectors of length n whose longest run of consecutive 1's has length k, for n >= 0, 0 <= k <= n. OEIS:A048004
Code
def statistic(w):
     if len(w) == 0:
         return 0
     if w[0] == 1:
         c = Composition(w.delta())[::2]
     else:
         c = Composition(w.delta())[1::2]
     return max(c + [0])

Created
Feb 12, 2016 at 22:11 by Martin Rubey
Updated
Dec 12, 2017 at 14:52 by Martin Rubey