Identifier
Identifier
Values
0 => 1
1 => 1
00 => 2
01 => 1
10 => 1
11 => 2
000 => 3
001 => 2
010 => 2
011 => 2
100 => 2
101 => 2
110 => 2
111 => 3
0000 => 4
0001 => 3
0010 => 2
0011 => 2
0100 => 2
0101 => 3
0110 => 2
0111 => 3
1000 => 3
1001 => 2
1010 => 3
1011 => 2
1100 => 2
1101 => 2
1110 => 3
1111 => 4
00000 => 5
00001 => 4
00010 => 3
00011 => 3
00100 => 3
00101 => 3
00110 => 2
00111 => 3
01000 => 3
01001 => 3
01010 => 4
01011 => 3
01100 => 2
01101 => 3
01110 => 3
01111 => 4
10000 => 4
10001 => 3
10010 => 3
10011 => 2
10100 => 3
10101 => 4
10110 => 3
10111 => 3
11000 => 3
11001 => 2
11010 => 3
11011 => 3
11100 => 3
11101 => 3
11110 => 4
11111 => 5
000000 => 6
000001 => 5
000010 => 4
000011 => 4
000100 => 3
000101 => 3
000110 => 3
000111 => 3
001000 => 3
001001 => 4
001010 => 4
001011 => 3
001100 => 3
001101 => 3
001110 => 3
001111 => 4
010000 => 4
010001 => 3
010010 => 4
010011 => 3
010100 => 4
010101 => 5
010110 => 3
010111 => 3
011000 => 3
011001 => 3
011010 => 3
011011 => 4
011100 => 3
011101 => 3
011110 => 4
011111 => 5
100000 => 5
100001 => 4
100010 => 3
100011 => 3
100100 => 4
100101 => 3
100110 => 3
100111 => 3
101000 => 3
101001 => 3
101010 => 5
101011 => 4
101100 => 3
101101 => 4
101110 => 3
101111 => 4
110000 => 4
110001 => 3
110010 => 3
110011 => 3
110100 => 3
110101 => 4
110110 => 4
110111 => 3
111000 => 3
111001 => 3
111010 => 3
111011 => 3
111100 => 4
111101 => 4
111110 => 5
111111 => 6
0000000 => 7
0000001 => 6
0000010 => 5
0000011 => 5
0000100 => 4
0000101 => 4
0000110 => 4
0000111 => 4
0001000 => 4
0001001 => 4
0001010 => 4
0001011 => 3
0001100 => 3
0001101 => 3
0001110 => 3
0001111 => 4
0010000 => 4
0010001 => 4
0010010 => 5
0010011 => 4
0010100 => 4
0010101 => 5
0010110 => 3
0010111 => 3
0011000 => 3
0011001 => 4
0011010 => 3
0011011 => 4
0011100 => 3
0011101 => 3
0011110 => 4
0011111 => 5
0100000 => 5
0100001 => 4
0100010 => 4
0100011 => 3
0100100 => 5
0100101 => 4
0100110 => 3
0100111 => 3
0101000 => 4
0101001 => 4
0101010 => 6
0101011 => 5
0101100 => 3
0101101 => 4
0101110 => 3
0101111 => 4
0110000 => 4
0110001 => 3
0110010 => 3
0110011 => 4
0110100 => 3
0110101 => 4
0110110 => 5
0110111 => 4
0111000 => 3
0111001 => 3
0111010 => 3
0111011 => 4
0111100 => 4
0111101 => 4
0111110 => 5
0111111 => 6
1000000 => 6
1000001 => 5
1000010 => 4
1000011 => 4
1000100 => 4
1000101 => 3
1000110 => 3
1000111 => 3
1001000 => 4
1001001 => 5
1001010 => 4
1001011 => 3
1001100 => 4
1001101 => 3
1001110 => 3
1001111 => 4
1010000 => 4
1010001 => 3
1010010 => 4
1010011 => 3
1010100 => 5
1010101 => 6
1010110 => 4
1010111 => 4
1011000 => 3
1011001 => 3
1011010 => 4
1011011 => 5
1011100 => 3
1011101 => 4
1011110 => 4
1011111 => 5
1100000 => 5
1100001 => 4
1100010 => 3
1100011 => 3
1100100 => 4
1100101 => 3
1100110 => 4
1100111 => 3
1101000 => 3
1101001 => 3
1101010 => 5
1101011 => 4
1101100 => 4
1101101 => 5
1101110 => 4
1101111 => 4
1110000 => 4
1110001 => 3
1110010 => 3
1110011 => 3
1110100 => 3
1110101 => 4
1110110 => 4
1110111 => 4
1111000 => 4
1111001 => 4
1111010 => 4
1111011 => 4
1111100 => 5
1111101 => 5
1111110 => 6
1111111 => 7
00000000 => 8
00000001 => 7
00000010 => 6
00000011 => 6
00000100 => 5
00000101 => 5
00000110 => 5
00000111 => 5
00001000 => 4
00001001 => 4
00001010 => 4
00001011 => 4
00001100 => 4
00001101 => 4
00001110 => 4
00001111 => 4
00010000 => 4
00010001 => 5
00010010 => 5
00010011 => 4
00010100 => 4
00010101 => 5
00010110 => 3
00010111 => 3
00011000 => 4
00011001 => 4
00011010 => 3
00011011 => 4
00011100 => 3
00011101 => 3
00011110 => 4
00011111 => 5
00100000 => 5
00100001 => 4
00100010 => 5
00100011 => 4
00100100 => 6
00100101 => 5
00100110 => 4
00100111 => 4
00101000 => 4
00101001 => 4
00101010 => 6
00101011 => 5
00101100 => 3
00101101 => 4
00101110 => 3
00101111 => 4
00110000 => 4
00110001 => 4
00110010 => 4
00110011 => 5
00110100 => 3
00110101 => 4
00110110 => 5
00110111 => 4
00111000 => 3
00111001 => 4
00111010 => 3
00111011 => 4
00111100 => 4
00111101 => 4
00111110 => 5
00111111 => 6
01000000 => 6
01000001 => 5
01000010 => 4
01000011 => 4
01000100 => 5
01000101 => 4
01000110 => 3
01000111 => 3
01001000 => 5
01001001 => 6
01001010 => 4
01001011 => 4
01001100 => 4
01001101 => 3
01001110 => 3
01001111 => 4
01010000 => 4
01010001 => 4
01010010 => 4
01010011 => 4
01010100 => 6
01010101 => 7
01010110 => 5
01010111 => 5
01011000 => 3
01011001 => 3
01011010 => 4
01011011 => 5
01011100 => 3
01011101 => 4
01011110 => 4
01011111 => 5
01100000 => 5
01100001 => 4
01100010 => 3
01100011 => 4
01100100 => 4
01100101 => 3
01100110 => 5
01100111 => 4
01101000 => 3
01101001 => 3
01101010 => 5
01101011 => 4
01101100 => 5
01101101 => 6
01101110 => 4
01101111 => 4
01110000 => 4
01110001 => 3
01110010 => 3
01110011 => 4
01110100 => 3
01110101 => 4
01110110 => 4
01110111 => 5
01111000 => 4
01111001 => 4
01111010 => 4
01111011 => 4
01111100 => 5
01111101 => 5
01111110 => 6
01111111 => 7
10000000 => 7
10000001 => 6
10000010 => 5
10000011 => 5
10000100 => 4
10000101 => 4
10000110 => 4
10000111 => 4
10001000 => 5
10001001 => 4
10001010 => 4
10001011 => 3
10001100 => 4
10001101 => 3
10001110 => 3
10001111 => 4
10010000 => 4
10010001 => 4
10010010 => 6
10010011 => 5
10010100 => 4
10010101 => 5
10010110 => 3
10010111 => 3
10011000 => 4
10011001 => 5
10011010 => 3
10011011 => 4
10011100 => 4
10011101 => 3
10011110 => 4
10011111 => 5
10100000 => 5
10100001 => 4
10100010 => 4
10100011 => 3
10100100 => 5
10100101 => 4
10100110 => 3
10100111 => 3
10101000 => 5
10101001 => 5
10101010 => 7
10101011 => 6
10101100 => 4
10101101 => 4
10101110 => 4
10101111 => 4
10110000 => 4
10110001 => 3
10110010 => 3
10110011 => 4
10110100 => 4
10110101 => 4
10110110 => 6
10110111 => 5
10111000 => 3
10111001 => 3
10111010 => 4
10111011 => 5
10111100 => 4
10111101 => 4
10111110 => 5
10111111 => 6
11000000 => 6
11000001 => 5
11000010 => 4
11000011 => 4
11000100 => 4
11000101 => 3
11000110 => 4
11000111 => 3
11001000 => 4
11001001 => 5
11001010 => 4
11001011 => 3
11001100 => 5
11001101 => 4
11001110 => 4
11001111 => 4
11010000 => 4
11010001 => 3
11010010 => 4
11010011 => 3
11010100 => 5
11010101 => 6
11010110 => 4
11010111 => 4
11011000 => 4
11011001 => 4
11011010 => 5
11011011 => 6
11011100 => 4
11011101 => 5
11011110 => 4
11011111 => 5
11100000 => 5
11100001 => 4
11100010 => 3
11100011 => 3
11100100 => 4
11100101 => 3
11100110 => 4
11100111 => 4
11101000 => 3
11101001 => 3
11101010 => 5
11101011 => 4
11101100 => 4
11101101 => 5
11101110 => 5
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 => 9
000000001 => 8
000000010 => 7
000000011 => 7
000000100 => 6
000000101 => 6
000000110 => 6
000000111 => 6
000001000 => 5
000001001 => 5
000001010 => 5
000001011 => 5
000001100 => 5
000001101 => 5
000001110 => 5
000001111 => 5
000010000 => 5
000010001 => 5
000010010 => 5
000010011 => 4
000010100 => 4
000010101 => 5
000010110 => 4
000010111 => 4
000011000 => 4
000011001 => 4
000011010 => 4
000011011 => 4
000011100 => 4
000011101 => 4
000011110 => 4
000011111 => 5
000100000 => 5
000100001 => 5
000100010 => 6
000100011 => 5
000100100 => 6
000100101 => 5
000100110 => 4
000100111 => 4
000101000 => 4
000101001 => 4
000101010 => 6
000101011 => 5
000101100 => 3
000101101 => 4
000101110 => 3
000101111 => 4
000110000 => 4
000110001 => 5
000110010 => 4
000110011 => 5
000110100 => 3
000110101 => 4
000110110 => 5
000110111 => 4
000111000 => 4
000111001 => 4
000111010 => 3
000111011 => 4
000111100 => 4
000111101 => 4
000111110 => 5
000111111 => 6
001000000 => 6
001000001 => 5
001000010 => 5
001000011 => 4
001000100 => 6
001000101 => 5
001000110 => 4
001000111 => 4
001001000 => 6
001001001 => 7
001001010 => 5
001001011 => 5
001001100 => 4
001001101 => 4
001001110 => 4
001001111 => 4
001010000 => 4
001010001 => 4
001010010 => 5
001010011 => 4
001010100 => 6
001010101 => 7
001010110 => 5
001010111 => 5
001011000 => 3
001011001 => 4
001011010 => 4
001011011 => 5
001011100 => 3
001011101 => 4
001011110 => 4
001011111 => 5
001100000 => 5
001100001 => 4
001100010 => 4
001100011 => 5
001100100 => 4
001100101 => 4
001100110 => 6
001100111 => 5
001101000 => 3
001101001 => 4
001101010 => 5
001101011 => 4
001101100 => 5
001101101 => 6
001101110 => 4
001101111 => 4
001110000 => 4
001110001 => 4
001110010 => 4
001110011 => 5
001110100 => 3
001110101 => 4
001110110 => 4
001110111 => 5
001111000 => 4
001111001 => 4
001111010 => 4
001111011 => 4
001111100 => 5
001111101 => 5
001111110 => 6
001111111 => 7
010000000 => 7
010000001 => 6
010000010 => 5
010000011 => 5
010000100 => 5
010000101 => 4
010000110 => 4
010000111 => 4
010001000 => 6
010001001 => 5
010001010 => 4
010001011 => 4
010001100 => 4
010001101 => 3
010001110 => 3
010001111 => 4
010010000 => 5
010010001 => 5
010010010 => 7
010010011 => 6
010010100 => 5
010010101 => 5
010010110 => 4
010010111 => 4
010011000 => 4
010011001 => 5
010011010 => 4
010011011 => 4
010011100 => 4
010011101 => 3
010011110 => 4
010011111 => 5
010100000 => 5
010100001 => 4
010100010 => 4
010100011 => 4
010100100 => 5
010100101 => 5
010100110 => 4
010100111 => 4
010101000 => 6
010101001 => 6
010101010 => 8
010101011 => 7
010101100 => 5
010101101 => 5
010101110 => 5
010101111 => 5
010110000 => 4
010110001 => 3
010110010 => 4
010110011 => 4
010110100 => 4
010110101 => 5
010110110 => 6
010110111 => 5
010111000 => 3
010111001 => 3
010111010 => 4
010111011 => 5
010111100 => 4
010111101 => 4
010111110 => 5
010111111 => 6
011000000 => 6
011000001 => 5
011000010 => 4
011000011 => 4
011000100 => 4
011000101 => 3
011000110 => 5
011000111 => 4
011001000 => 4
011001001 => 5
011001010 => 4
011001011 => 4
011001100 => 6
011001101 => 5
011001110 => 4
011001111 => 4
011010000 => 4
011010001 => 3
011010010 => 4
011010011 => 4
011010100 => 5
011010101 => 6
011010110 => 5
011010111 => 4
011011000 => 5
011011001 => 5
011011010 => 6
011011011 => 7
011011100 => 4
011011101 => 5
011011110 => 4
011011111 => 5
011100000 => 5
011100001 => 4
011100010 => 3
011100011 => 4
011100100 => 4
011100101 => 3
011100110 => 4
011100111 => 5
011101000 => 3
011101001 => 3
011101010 => 5
011101011 => 4
011101100 => 4
011101101 => 5
011101110 => 6
011101111 => 5
011110000 => 4
011110001 => 4
011110010 => 4
011110011 => 4
011110100 => 4
011110101 => 4
011110110 => 4
011110111 => 5
011111000 => 5
011111001 => 5
011111010 => 5
011111011 => 5
011111100 => 6
011111101 => 6
011111110 => 7
011111111 => 8
100000000 => 8
100000001 => 7
100000010 => 6
100000011 => 6
100000100 => 5
100000101 => 5
100000110 => 5
100000111 => 5
100001000 => 5
100001001 => 4
100001010 => 4
100001011 => 4
100001100 => 4
100001101 => 4
100001110 => 4
100001111 => 4
100010000 => 5
100010001 => 6
100010010 => 5
100010011 => 4
100010100 => 4
100010101 => 5
100010110 => 3
100010111 => 3
100011000 => 5
100011001 => 4
100011010 => 3
100011011 => 4
100011100 => 4
100011101 => 3
100011110 => 4
100011111 => 5
100100000 => 5
100100001 => 4
100100010 => 5
100100011 => 4
100100100 => 7
100100101 => 6
100100110 => 5
100100111 => 5
100101000 => 4
100101001 => 5
100101010 => 6
100101011 => 5
100101100 => 4
100101101 => 4
100101110 => 3
100101111 => 4
100110000 => 4
100110001 => 4
100110010 => 5
100110011 => 6
100110100 => 4
100110101 => 4
100110110 => 5
100110111 => 4
100111000 => 4
100111001 => 5
100111010 => 3
100111011 => 4
100111100 => 4
100111101 => 4
100111110 => 5
100111111 => 6
101000000 => 6
101000001 => 5
101000010 => 4
101000011 => 4
101000100 => 5
101000101 => 4
101000110 => 3
101000111 => 3
101001000 => 5
101001001 => 6
101001010 => 5
101001011 => 4
101001100 => 4
101001101 => 4
101001110 => 3
101001111 => 4
101010000 => 5
101010001 => 5
101010010 => 5
101010011 => 5
101010100 => 7
101010101 => 8
101010110 => 6
101010111 => 6
101011000 => 4
101011001 => 4
101011010 => 5
101011011 => 5
101011100 => 4
101011101 => 4
101011110 => 4
101011111 => 5
101100000 => 5
101100001 => 4
101100010 => 3
101100011 => 4
101100100 => 4
101100101 => 4
101100110 => 5
101100111 => 4
101101000 => 4
101101001 => 4
101101010 => 5
101101011 => 5
101101100 => 6
101101101 => 7
101101110 => 5
101101111 => 5
101110000 => 4
101110001 => 3
101110010 => 3
101110011 => 4
101110100 => 4
101110101 => 4
101110110 => 5
101110111 => 6
101111000 => 4
101111001 => 4
101111010 => 4
101111011 => 5
101111100 => 5
101111101 => 5
101111110 => 6
101111111 => 7
110000000 => 7
110000001 => 6
110000010 => 5
110000011 => 5
110000100 => 4
110000101 => 4
110000110 => 4
110000111 => 4
110001000 => 5
110001001 => 4
110001010 => 4
110001011 => 3
110001100 => 5
110001101 => 4
110001110 => 4
110001111 => 4
110010000 => 4
110010001 => 4
110010010 => 6
110010011 => 5
110010100 => 4
110010101 => 5
110010110 => 4
110010111 => 3
110011000 => 5
110011001 => 6
110011010 => 4
110011011 => 4
110011100 => 5
110011101 => 4
110011110 => 4
110011111 => 5
110100000 => 5
110100001 => 4
110100010 => 4
110100011 => 3
110100100 => 5
110100101 => 4
110100110 => 4
110100111 => 3
110101000 => 5
110101001 => 5
110101010 => 7
110101011 => 6
110101100 => 4
110101101 => 5
110101110 => 4
110101111 => 4
110110000 => 4
110110001 => 4
110110010 => 4
110110011 => 4
110110100 => 5
110110101 => 5
110110110 => 7
110110111 => 6
110111000 => 4
110111001 => 4
110111010 => 5
110111011 => 6
110111100 => 4
110111101 => 5
110111110 => 5
110111111 => 6
111000000 => 6
111000001 => 5
111000010 => 4
111000011 => 4
111000100 => 4
111000101 => 3
111000110 => 4
111000111 => 4
111001000 => 4
111001001 => 5
111001010 => 4
111001011 => 3
111001100 => 5
111001101 => 4
111001110 => 5
111001111 => 4
111010000 => 4
111010001 => 3
111010010 => 4
111010011 => 3
111010100 => 5
111010101 => 6
111010110 => 4
111010111 => 4
111011000 => 4
111011001 => 4
111011010 => 5
111011011 => 6
111011100 => 5
111011101 => 6
111011110 => 5
111011111 => 5
111100000 => 5
111100001 => 4
111100010 => 4
111100011 => 4
111100100 => 4
111100101 => 4
111100110 => 4
111100111 => 4
111101000 => 4
111101001 => 4
111101010 => 5
111101011 => 4
111101100 => 4
111101101 => 5
111101110 => 5
111101111 => 5
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
0000000000 => 10
0000000001 => 9
0000000010 => 8
0000000011 => 8
0000000100 => 7
0000000101 => 7
0000000110 => 7
0000000111 => 7
0000001000 => 6
0000001001 => 6
0000001010 => 6
0000001011 => 6
0000001100 => 6
0000001101 => 6
0000001110 => 6
0000001111 => 6
0000010000 => 5
0000010001 => 5
0000010010 => 5
0000010011 => 5
0000010100 => 5
0000010101 => 5
0000010110 => 5
0000010111 => 5
0000011000 => 5
0000011001 => 5
0000011010 => 5
0000011011 => 5
0000011100 => 5
0000011101 => 5
0000011110 => 5
0000011111 => 5
0000100000 => 5
0000100001 => 6
0000100010 => 6
0000100011 => 5
0000100100 => 6
0000100101 => 5
0000100110 => 4
0000100111 => 4
0000101000 => 4
0000101001 => 4
0000101010 => 6
0000101011 => 5
0000101100 => 4
0000101101 => 4
0000101110 => 4
0000101111 => 4
0000110000 => 5
0000110001 => 5
0000110010 => 4
0000110011 => 5
0000110100 => 4
0000110101 => 4
0000110110 => 5
0000110111 => 4
0000111000 => 4
0000111001 => 4
0000111010 => 4
0000111011 => 4
0000111100 => 4
0000111101 => 4
0000111110 => 5
0000111111 => 6
0001000000 => 6
0001000001 => 5
0001000010 => 6
0001000011 => 5
0001000100 => 7
0001000101 => 6
0001000110 => 5
0001000111 => 5
0001001000 => 6
0001001001 => 7
0001001010 => 5
0001001011 => 5
0001001100 => 4
0001001101 => 4
0001001110 => 4
0001001111 => 4
0001010000 => 4
0001010001 => 5
0001010010 => 5
0001010011 => 4
0001010100 => 6
0001010101 => 7
0001010110 => 5
0001010111 => 5
0001011000 => 4
0001011001 => 4
0001011010 => 4
0001011011 => 5
0001011100 => 3
0001011101 => 4
0001011110 => 4
0001011111 => 5
0001100000 => 5
0001100001 => 5
0001100010 => 5
0001100011 => 6
0001100100 => 4
0001100101 => 4
0001100110 => 6
0001100111 => 5
0001101000 => 4
0001101001 => 4
0001101010 => 5
0001101011 => 4
0001101100 => 5
0001101101 => 6
0001101110 => 4
0001101111 => 4
0001110000 => 4
0001110001 => 5
0001110010 => 4
0001110011 => 5
0001110100 => 3
0001110101 => 4
0001110110 => 4
0001110111 => 5
0001111000 => 4
0001111001 => 4
0001111010 => 4
0001111011 => 4
0001111100 => 5
0001111101 => 5
0001111110 => 6
0001111111 => 7
0010000000 => 7
0010000001 => 6
0010000010 => 5
0010000011 => 5
0010000100 => 6
0010000101 => 5
0010000110 => 4
0010000111 => 4
0010001000 => 7
0010001001 => 6
0010001010 => 5
0010001011 => 5
0010001100 => 4
0010001101 => 4
0010001110 => 4
0010001111 => 4
0010010000 => 6
0010010001 => 6
0010010010 => 8
0010010011 => 7
0010010100 => 5
0010010101 => 5
0010010110 => 5
0010010111 => 5
0010011000 => 4
0010011001 => 5
0010011010 => 4
0010011011 => 4
0010011100 => 4
0010011101 => 4
0010011110 => 4
0010011111 => 5
0010100000 => 5
0010100001 => 4
0010100010 => 5
0010100011 => 4
0010100100 => 5
0010100101 => 6
0010100110 => 4
0010100111 => 4
0010101000 => 6
0010101001 => 6
0010101010 => 8
0010101011 => 7
0010101100 => 5
0010101101 => 5
0010101110 => 5
0010101111 => 5
0010110000 => 4
0010110001 => 4
click to show generating function       
Description
The minimal number such that all substrings of this length are unique.
References
[1] Aumayr, W. String with all unique substrings MathOverflow:277790
Code
def statistic(w):
    for k in range(1,len(w)+1):
        S = []
        for i in range(len(w)-k+1):
            s = w[i:i+k]
            if s in S:
                break
            else:
                S.append(s)
        else:
            return k

Created
Aug 02, 2017 at 17:04 by Martin Rubey
Updated
Aug 02, 2017 at 17:04 by Martin Rubey