***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St001437 ----------------------------------------------------------------------------- Collection: Binary words ----------------------------------------------------------------------------- Description: The flex of a binary word. This is the product of the lex statistic ([[St001436]], augmented by 1) and its frequency ([[St000627]]), see [1, ยง8]. ----------------------------------------------------------------------------- References: [1] Ahlbach, C., Swanson, J. P. Refined cyclic sieving on words for the major index statistic [[MathSciNet:3836732]] ----------------------------------------------------------------------------- Code: def lex(w): orbit = [ tuple(w[i:] + w[:i]) for i in range(len(w)) ] return sorted(set(orbit)).index(tuple(w))+1 def freq(w): w = list(w) n = len(w) for i in sorted(Integer(n).divisors()): if w == w[:i]*(n//i): return n // i def statistic(w): return lex(w)*freq(w) ----------------------------------------------------------------------------- Statistic values: 0 => 1 1 => 1 00 => 2 01 => 1 10 => 2 11 => 2 000 => 3 001 => 1 010 => 2 011 => 1 100 => 3 101 => 2 110 => 3 111 => 3 0000 => 4 0001 => 1 0010 => 2 0011 => 1 0100 => 3 0101 => 2 0110 => 2 0111 => 1 1000 => 4 1001 => 3 1010 => 4 1011 => 2 1100 => 4 1101 => 3 1110 => 4 1111 => 4 00000 => 5 00001 => 1 00010 => 2 00011 => 1 00100 => 3 00101 => 1 00110 => 2 00111 => 1 01000 => 4 01001 => 2 01010 => 3 01011 => 1 01100 => 3 01101 => 2 01110 => 2 01111 => 1 10000 => 5 10001 => 4 10010 => 4 10011 => 3 10100 => 5 10101 => 3 10110 => 4 10111 => 2 11000 => 5 11001 => 4 11010 => 5 11011 => 3 11100 => 5 11101 => 4 11110 => 5 11111 => 5 000000 => 6 000001 => 1 000010 => 2 000011 => 1 000100 => 3 000101 => 1 000110 => 2 000111 => 1 001000 => 4 001001 => 2 001010 => 2 001011 => 1 001100 => 3 001101 => 1 001110 => 2 001111 => 1 010000 => 5 010001 => 3 010010 => 4 010011 => 2 010100 => 4 010101 => 3 010110 => 2 010111 => 1 011000 => 4 011001 => 3 011010 => 3 011011 => 2 011100 => 3 011101 => 2 011110 => 2 011111 => 1 100000 => 6 100001 => 5 100010 => 5 100011 => 4 100100 => 6 100101 => 4 100110 => 4 100111 => 3 101000 => 6 101001 => 5 101010 => 6 101011 => 3 101100 => 5 101101 => 4 101110 => 4 101111 => 2 110000 => 6 110001 => 5 110010 => 6 110011 => 4 110100 => 6 110101 => 5 110110 => 6 110111 => 3 111000 => 6 111001 => 5 111010 => 6 111011 => 4 111100 => 6 111101 => 5 111110 => 6 111111 => 6 0000000 => 7 0000001 => 1 0000010 => 2 0000011 => 1 0000100 => 3 0000101 => 1 0000110 => 2 0000111 => 1 0001000 => 4 0001001 => 1 0001010 => 2 0001011 => 1 0001100 => 3 0001101 => 1 0001110 => 2 0001111 => 1 0010000 => 5 0010001 => 2 0010010 => 3 0010011 => 1 0010100 => 3 0010101 => 1 0010110 => 2 0010111 => 1 0011000 => 4 0011001 => 2 0011010 => 2 0011011 => 1 0011100 => 3 0011101 => 1 0011110 => 2 0011111 => 1 0100000 => 6 0100001 => 4 0100010 => 4 0100011 => 3 0100100 => 5 0100101 => 2 0100110 => 3 0100111 => 2 0101000 => 5 0101001 => 3 0101010 => 4 0101011 => 1 0101100 => 3 0101101 => 2 0101110 => 2 0101111 => 1 0110000 => 5 0110001 => 4 0110010 => 4 0110011 => 2 0110100 => 4 0110101 => 3 0110110 => 3 0110111 => 1 0111000 => 4 0111001 => 3 0111010 => 3 0111011 => 2 0111100 => 3 0111101 => 2 0111110 => 2 0111111 => 1 1000000 => 7 1000001 => 6 1000010 => 6 1000011 => 5 1000100 => 6 1000101 => 5 1000110 => 5 1000111 => 4 1001000 => 7 1001001 => 5 1001010 => 5 1001011 => 4 1001100 => 6 1001101 => 4 1001110 => 4 1001111 => 3 1010000 => 7 1010001 => 6 1010010 => 6 1010011 => 5 1010100 => 7 1010101 => 4 1010110 => 5 1010111 => 3 1011000 => 6 1011001 => 5 1011010 => 6 1011011 => 3 1011100 => 5 1011101 => 4 1011110 => 4 1011111 => 2 1100000 => 7 1100001 => 6 1100010 => 7 1100011 => 5 1100100 => 7 1100101 => 6 1100110 => 6 1100111 => 4 1101000 => 7 1101001 => 6 1101010 => 7 1101011 => 5 1101100 => 7 1101101 => 5 1101110 => 6 1101111 => 3 1110000 => 7 1110001 => 6 1110010 => 7 1110011 => 5 1110100 => 7 1110101 => 6 1110110 => 7 1110111 => 4 1111000 => 7 1111001 => 6 1111010 => 7 1111011 => 5 1111100 => 7 1111101 => 6 1111110 => 7 1111111 => 7 00000000 => 8 00000001 => 1 00000010 => 2 00000011 => 1 00000100 => 3 00000101 => 1 00000110 => 2 00000111 => 1 00001000 => 4 00001001 => 1 00001010 => 2 00001011 => 1 00001100 => 3 00001101 => 1 00001110 => 2 00001111 => 1 00010000 => 5 00010001 => 2 00010010 => 2 00010011 => 1 00010100 => 3 00010101 => 1 00010110 => 2 00010111 => 1 00011000 => 4 00011001 => 1 00011010 => 2 00011011 => 1 00011100 => 3 00011101 => 1 00011110 => 2 00011111 => 1 00100000 => 6 00100001 => 3 00100010 => 4 00100011 => 2 00100100 => 4 00100101 => 1 00100110 => 2 00100111 => 1 00101000 => 4 00101001 => 2 00101010 => 2 00101011 => 1 00101100 => 3 00101101 => 1 00101110 => 2 00101111 => 1 00110000 => 5 00110001 => 3 00110010 => 3 00110011 => 2 00110100 => 3 00110101 => 1 00110110 => 2 00110111 => 1 00111000 => 4 00111001 => 2 00111010 => 2 00111011 => 1 00111100 => 3 00111101 => 1 00111110 => 2 00111111 => 1 01000000 => 7 01000001 => 5 01000010 => 5 01000011 => 4 01000100 => 6 01000101 => 3 01000110 => 4 01000111 => 3 01001000 => 6 01001001 => 3 01001010 => 4 01001011 => 2 01001100 => 4 01001101 => 2 01001110 => 3 01001111 => 2 01010000 => 6 01010001 => 4 01010010 => 5 01010011 => 3 01010100 => 5 01010101 => 4 01010110 => 2 01010111 => 1 01011000 => 4 01011001 => 3 01011010 => 3 01011011 => 1 01011100 => 3 01011101 => 2 01011110 => 2 01011111 => 1 01100000 => 6 01100001 => 5 01100010 => 5 01100011 => 3 01100100 => 5 01100101 => 4 01100110 => 4 01100111 => 2 01101000 => 5 01101001 => 4 01101010 => 4 01101011 => 2 01101100 => 4 01101101 => 3 01101110 => 2 01101111 => 1 01110000 => 5 01110001 => 4 01110010 => 4 01110011 => 3 01110100 => 4 01110101 => 3 01110110 => 3 01110111 => 2 01111000 => 4 01111001 => 3 01111010 => 3 01111011 => 2 01111100 => 3 01111101 => 2 01111110 => 2 01111111 => 1 10000000 => 8 10000001 => 7 10000010 => 7 10000011 => 6 10000100 => 7 10000101 => 6 10000110 => 6 10000111 => 5 10001000 => 8 10001001 => 6 10001010 => 6 10001011 => 5 10001100 => 6 10001101 => 5 10001110 => 5 10001111 => 4 10010000 => 8 10010001 => 7 10010010 => 6 10010011 => 5 10010100 => 7 10010101 => 5 10010110 => 5 10010111 => 4 10011000 => 7 10011001 => 6 10011010 => 5 10011011 => 4 10011100 => 6 10011101 => 4 10011110 => 4 10011111 => 3 10100000 => 8 10100001 => 7 10100010 => 7 10100011 => 6 10100100 => 8 10100101 => 6 10100110 => 6 10100111 => 5 10101000 => 8 10101001 => 7 10101010 => 8 10101011 => 4 10101100 => 6 10101101 => 4 10101110 => 5 10101111 => 3 10110000 => 7 10110001 => 6 10110010 => 7 10110011 => 5 10110100 => 7 10110101 => 5 10110110 => 6 10110111 => 3 10111000 => 6 10111001 => 5 10111010 => 6 10111011 => 4 10111100 => 5 10111101 => 4 10111110 => 4 10111111 => 2 11000000 => 8 11000001 => 7 11000010 => 8 11000011 => 6 11000100 => 8 11000101 => 7 11000110 => 7 11000111 => 5 11001000 => 8 11001001 => 7 11001010 => 8 11001011 => 6 11001100 => 8 11001101 => 6 11001110 => 6 11001111 => 4 11010000 => 8 11010001 => 7 11010010 => 8 11010011 => 6 11010100 => 8 11010101 => 7 11010110 => 7 11010111 => 5 11011000 => 8 11011001 => 7 11011010 => 8 11011011 => 5 11011100 => 7 11011101 => 6 11011110 => 6 11011111 => 3 11100000 => 8 11100001 => 7 11100010 => 8 11100011 => 6 11100100 => 8 11100101 => 7 11100110 => 8 11100111 => 5 11101000 => 8 11101001 => 7 11101010 => 8 11101011 => 6 11101100 => 8 11101101 => 7 11101110 => 8 11101111 => 4 11110000 => 8 11110001 => 7 11110010 => 8 11110011 => 6 11110100 => 8 11110101 => 7 11110110 => 8 11110111 => 5 11111000 => 8 11111001 => 7 11111010 => 8 11111011 => 6 11111100 => 8 11111101 => 7 11111110 => 8 11111111 => 8 000000000 => 9 000000001 => 1 000000010 => 2 000000011 => 1 000000100 => 3 000000101 => 1 000000110 => 2 000000111 => 1 000001000 => 4 000001001 => 1 000001010 => 2 000001011 => 1 000001100 => 3 000001101 => 1 000001110 => 2 000001111 => 1 000010000 => 5 000010001 => 1 000010010 => 2 000010011 => 1 000010100 => 3 000010101 => 1 000010110 => 2 000010111 => 1 000011000 => 4 000011001 => 1 000011010 => 2 000011011 => 1 000011100 => 3 000011101 => 1 000011110 => 2 000011111 => 1 000100000 => 6 000100001 => 2 000100010 => 3 000100011 => 1 000100100 => 3 000100101 => 1 000100110 => 2 000100111 => 1 000101000 => 4 000101001 => 1 000101010 => 2 000101011 => 1 000101100 => 3 000101101 => 1 000101110 => 2 000101111 => 1 000110000 => 5 000110001 => 2 000110010 => 2 000110011 => 1 000110100 => 3 000110101 => 1 000110110 => 2 000110111 => 1 000111000 => 4 000111001 => 1 000111010 => 2 000111011 => 1 000111100 => 3 000111101 => 1 000111110 => 2 000111111 => 1 001000000 => 7 001000001 => 4 001000010 => 4 001000011 => 3 001000100 => 5 001000101 => 2 001000110 => 3 001000111 => 2 001001000 => 5 001001001 => 3 001001010 => 2 001001011 => 1 001001100 => 3 001001101 => 1 001001110 => 2 001001111 => 1 001010000 => 5 001010001 => 3 001010010 => 3 001010011 => 1 001010100 => 3 001010101 => 1 001010110 => 2 001010111 => 1 001011000 => 4 001011001 => 2 001011010 => 2 001011011 => 1 001011100 => 3 001011101 => 1 001011110 => 2 001011111 => 1 001100000 => 6 001100001 => 4 001100010 => 4 001100011 => 2 001100100 => 4 001100101 => 2 001100110 => 3 001100111 => 1 001101000 => 4 001101001 => 2 001101010 => 2 001101011 => 1 001101100 => 3 001101101 => 1 001101110 => 2 001101111 => 1 001110000 => 5 001110001 => 3 001110010 => 3 001110011 => 2 001110100 => 3 001110101 => 1 001110110 => 2 001110111 => 1 001111000 => 4 001111001 => 2 001111010 => 2 001111011 => 1 001111100 => 3 001111101 => 1 001111110 => 2 001111111 => 1 010000000 => 8 010000001 => 6 010000010 => 6 010000011 => 5 010000100 => 6 010000101 => 4 010000110 => 5 010000111 => 4 010001000 => 7 010001001 => 4 010001010 => 4 010001011 => 3 010001100 => 5 010001101 => 3 010001110 => 4 010001111 => 3 010010000 => 7 010010001 => 5 010010010 => 6 010010011 => 3 010010100 => 5 010010101 => 2 010010110 => 3 010010111 => 2 010011000 => 5 010011001 => 3 010011010 => 4 010011011 => 2 010011100 => 4 010011101 => 2 010011110 => 3 010011111 => 2 010100000 => 7 010100001 => 5 010100010 => 6 010100011 => 4 010100100 => 6 010100101 => 3 010100110 => 4 010100111 => 3 010101000 => 6 010101001 => 4 010101010 => 5 010101011 => 1 010101100 => 3 010101101 => 2 010101110 => 2 010101111 => 1 010110000 => 5 010110001 => 4 010110010 => 4 010110011 => 2 010110100 => 4 010110101 => 3 010110110 => 2 010110111 => 1 010111000 => 4 010111001 => 3 010111010 => 3 010111011 => 1 010111100 => 3 010111101 => 2 010111110 => 2 010111111 => 1 011000000 => 7 011000001 => 6 011000010 => 6 011000011 => 4 011000100 => 6 011000101 => 5 011000110 => 4 011000111 => 3 011001000 => 6 011001001 => 5 011001010 => 5 011001011 => 3 011001100 => 5 011001101 => 3 011001110 => 3 011001111 => 2 011010000 => 6 011010001 => 5 011010010 => 5 011010011 => 3 011010100 => 5 011010101 => 4 011010110 => 4 011010111 => 2 011011000 => 5 011011001 => 4 011011010 => 4 011011011 => 3 011011100 => 3 011011101 => 2 011011110 => 2 011011111 => 1 011100000 => 6 011100001 => 5 011100010 => 5 011100011 => 4 011100100 => 5 011100101 => 4 011100110 => 4 011100111 => 2 011101000 => 5 011101001 => 4 011101010 => 4 011101011 => 3 011101100 => 4 011101101 => 3 011101110 => 3 011101111 => 1 011110000 => 5 011110001 => 4 011110010 => 4 011110011 => 3 011110100 => 4 011110101 => 3 011110110 => 3 011110111 => 2 011111000 => 4 011111001 => 3 011111010 => 3 011111011 => 2 011111100 => 3 011111101 => 2 011111110 => 2 011111111 => 1 100000000 => 9 100000001 => 8 100000010 => 8 100000011 => 7 100000100 => 8 100000101 => 7 100000110 => 7 100000111 => 6 100001000 => 8 100001001 => 7 100001010 => 7 100001011 => 6 100001100 => 7 100001101 => 6 100001110 => 6 100001111 => 5 100010000 => 9 100010001 => 7 100010010 => 7 100010011 => 6 100010100 => 7 100010101 => 6 100010110 => 6 100010111 => 5 100011000 => 8 100011001 => 6 100011010 => 6 100011011 => 5 100011100 => 6 100011101 => 5 100011110 => 5 100011111 => 4 100100000 => 9 100100001 => 8 100100010 => 8 100100011 => 7 100100100 => 9 100100101 => 6 100100110 => 6 100100111 => 5 100101000 => 8 100101001 => 6 100101010 => 6 100101011 => 5 100101100 => 7 100101101 => 5 100101110 => 5 100101111 => 4 100110000 => 8 100110001 => 7 100110010 => 7 100110011 => 5 100110100 => 7 100110101 => 5 100110110 => 5 100110111 => 4 100111000 => 7 100111001 => 6 100111010 => 5 100111011 => 4 100111100 => 6 100111101 => 4 100111110 => 4 100111111 => 3 101000000 => 9 101000001 => 8 101000010 => 8 101000011 => 7 101000100 => 9 101000101 => 7 101000110 => 7 101000111 => 6 101001000 => 9 101001001 => 8 101001010 => 7 101001011 => 6 101001100 => 8 101001101 => 6 101001110 => 6 101001111 => 5 101010000 => 9 101010001 => 8 101010010 => 8 101010011 => 7 101010100 => 9 101010101 => 5 101010110 => 6 101010111 => 4 101011000 => 7 101011001 => 6 101011010 => 7 101011011 => 4 101011100 => 6 101011101 => 4 101011110 => 5 101011111 => 3 101100000 => 8 101100001 => 7 101100010 => 8 101100011 => 6 101100100 => 8 101100101 => 6 101100110 => 7 101100111 => 5 101101000 => 8 101101001 => 7 101101010 => 8 101101011 => 5 101101100 => 7 101101101 => 6 101101110 => 5 101101111 => 3 101110000 => 7 101110001 => 6 101110010 => 7 101110011 => 5 101110100 => 7 101110101 => 6 101110110 => 6 101110111 => 3 101111000 => 6 101111001 => 5 101111010 => 6 101111011 => 4 101111100 => 5 101111101 => 4 101111110 => 4 101111111 => 2 110000000 => 9 110000001 => 8 110000010 => 9 110000011 => 7 110000100 => 9 110000101 => 8 110000110 => 8 110000111 => 6 110001000 => 9 110001001 => 8 110001010 => 9 110001011 => 7 110001100 => 8 110001101 => 7 110001110 => 7 110001111 => 5 110010000 => 9 110010001 => 8 110010010 => 9 110010011 => 7 110010100 => 9 110010101 => 8 110010110 => 8 110010111 => 6 110011000 => 9 110011001 => 7 110011010 => 8 110011011 => 6 110011100 => 8 110011101 => 6 110011110 => 6 110011111 => 4 110100000 => 9 110100001 => 8 110100010 => 9 110100011 => 7 110100100 => 9 110100101 => 8 110100110 => 8 110100111 => 6 110101000 => 9 110101001 => 8 110101010 => 9 110101011 => 7 110101100 => 9 110101101 => 7 110101110 => 7 110101111 => 5 110110000 => 9 110110001 => 8 110110010 => 9 110110011 => 7 110110100 => 9 110110101 => 8 110110110 => 9 110110111 => 5 110111000 => 8 110111001 => 7 110111010 => 8 110111011 => 5 110111100 => 7 110111101 => 6 110111110 => 6 110111111 => 3 111000000 => 9 111000001 => 8 111000010 => 9 111000011 => 7 111000100 => 9 111000101 => 8 111000110 => 9 111000111 => 6 111001000 => 9 111001001 => 8 111001010 => 9 111001011 => 7 111001100 => 9 111001101 => 8 111001110 => 8 111001111 => 5 111010000 => 9 111010001 => 8 111010010 => 9 111010011 => 7 111010100 => 9 111010101 => 8 111010110 => 9 111010111 => 6 111011000 => 9 111011001 => 8 111011010 => 9 111011011 => 7 111011100 => 9 111011101 => 7 111011110 => 8 111011111 => 4 111100000 => 9 111100001 => 8 111100010 => 9 111100011 => 7 111100100 => 9 111100101 => 8 111100110 => 9 111100111 => 6 111101000 => 9 111101001 => 8 111101010 => 9 111101011 => 7 111101100 => 9 111101101 => 8 111101110 => 9 111101111 => 5 111110000 => 9 111110001 => 8 111110010 => 9 111110011 => 7 111110100 => 9 111110101 => 8 111110110 => 9 111110111 => 6 111111000 => 9 111111001 => 8 111111010 => 9 111111011 => 7 111111100 => 9 111111101 => 8 111111110 => 9 111111111 => 9 1010101010 => 10 1010101100 => 7 1010110010 => 8 1010110100 => 8 1010111000 => 7 1011001010 => 9 1011001100 => 8 1011010010 => 9 1011010100 => 9 1011011000 => 8 1011100010 => 8 1011100100 => 8 1011101000 => 8 1011110000 => 7 1100101010 => 10 1100101100 => 9 1100110010 => 10 1100110100 => 9 1100111000 => 9 1101001010 => 10 1101001100 => 10 1101010010 => 10 1101010100 => 10 1101011000 => 10 1101100010 => 10 1101100100 => 10 1101101000 => 10 1101110000 => 9 1110001010 => 10 1110001100 => 10 1110010010 => 10 1110010100 => 10 1110011000 => 10 1110100010 => 10 1110100100 => 10 1110101000 => 10 1110110000 => 10 1111000010 => 10 1111000100 => 10 1111001000 => 10 1111010000 => 10 1111100000 => 10 1111111110 => 10 1111111101 => 9 1111000001 => 9 1110111110 => 8 1110100001 => 9 1110011110 => 8 1110010001 => 9 1110001001 => 9 1110000101 => 9 1101111110 => 6 1101100001 => 9 1101010001 => 9 1101001110 => 8 1101001001 => 9 1101000101 => 9 1100110001 => 9 1100101001 => 9 1100100110 => 9 1100100101 => 9 1100011001 => 8 1100010101 => 9 1100010010 => 10 1100001000 => 10 1011111110 => 4 1011111101 => 4 1011100001 => 7 1011010001 => 8 1011001001 => 8 1011000101 => 7 1010111110 => 5 1010110001 => 7 1010101001 => 9 1010100110 => 8 1010100101 => 8 1010011010 => 7 1010011001 => 8 1010010110 => 7 1010010101 => 7 1010001110 => 7 1001111110 => 4 1001111000 => 7 1001110100 => 7 1001110001 => 7 1001101100 => 7 1001101010 => 6 1001101001 => 7 1001100110 => 6 1001100101 => 7 1001011110 => 5 1001011010 => 6 1001011001 => 6 1001010110 => 6 1001010101 => 6 1001001110 => 6 1000111110 => 5 1000111100 => 6 1000111010 => 6 1000110110 => 6 1000101110 => 6 1000011110 => 6 1000010110 => 7 1000001110 => 7 1000001010 => 8 1000000110 => 8 1000000100 => 9 1000000010 => 9 1000000000 => 10 10000000000 => 11 10000000010 => 10 10000000110 => 9 10000001110 => 8 10000011110 => 7 10000111110 => 6 10001111110 => 5 10011111110 => 4 10111111110 => 4 11111111110 => 11 10000000100 => 10 10000001010 => 9 10000010110 => 8 10000101110 => 7 10001011110 => 6 10010111110 => 5 10101111110 => 5 11011111110 => 6 10000010000 => 10 10000100010 => 9 10001000010 => 10 10000100100 => 9 10001001010 => 8 10001000100 => 9 10000101000 => 9 10010001010 => 9 10001010010 => 8 10010000100 => 10 10001001000 => 10 10010010010 => 8 10001010100 => 8 10010101010 => 7 10010001000 => 11 10100010010 => 10 10010100010 => 9 10010010100 => 9 10100101010 => 8 101010101010 => 12 101010101100 => 8 101010110010 => 9 101010110100 => 9 101010111000 => 8 101011001010 => 10 101011001100 => 9 101011010010 => 10 101011010100 => 10 101011011000 => 8 101011100010 => 9 101011100100 => 9 101011101000 => 9 101011110000 => 8 101100101010 => 11 101100101100 => 10 101100110010 => 10 101100110100 => 10 101100111000 => 9 101101001010 => 11 101101001100 => 10 101101010010 => 11 101101010100 => 11 101101011000 => 10 101101100010 => 10 101101100100 => 10 101101101000 => 10 101101110000 => 8 101110001010 => 10 101110001100 => 9 101110010010 => 10 101110010100 => 10 101110011000 => 9 101110100010 => 10 101110100100 => 10 101110101000 => 10 101110110000 => 9 101111000010 => 9 101111000100 => 9 101111001000 => 9 101111010000 => 9 101111100000 => 8 110010101010 => 12 110010101100 => 11 110010110010 => 12 110010110100 => 11 110010111000 => 11 110011001010 => 12 110011001100 => 12 110011010010 => 11 110011010100 => 11 110011011000 => 11 110011100010 => 11 110011100100 => 11 110011101000 => 10 110011110000 => 10 110100101010 => 12 110100101100 => 12 110100110010 => 12 110100110100 => 12 110100111000 => 11 110101001010 => 12 110101001100 => 12 110101010010 => 12 110101010100 => 12 110101011000 => 12 110101100010 => 12 110101100100 => 12 110101101000 => 12 110101110000 => 11 110110001010 => 12 110110001100 => 12 110110010010 => 12 110110010100 => 12 110110011000 => 12 110110100010 => 12 110110100100 => 12 110110101000 => 12 110110110000 => 12 110111000010 => 11 110111000100 => 11 110111001000 => 11 110111010000 => 11 110111100000 => 10 111000101010 => 12 111000101100 => 12 111000110010 => 12 111000110100 => 12 111000111000 => 12 111001001010 => 12 111001001100 => 12 111001010010 => 12 111001010100 => 12 111001011000 => 12 111001100010 => 12 111001100100 => 12 111001101000 => 12 111001110000 => 12 111010001010 => 12 111010001100 => 12 111010010010 => 12 111010010100 => 12 111010011000 => 12 111010100010 => 12 111010100100 => 12 111010101000 => 12 111010110000 => 12 111011000010 => 12 111011000100 => 12 111011001000 => 12 111011010000 => 12 111011100000 => 12 111100001010 => 12 111100001100 => 12 111100010010 => 12 111100010100 => 12 111100011000 => 12 111100100010 => 12 111100100100 => 12 111100101000 => 12 111100110000 => 12 111101000010 => 12 111101000100 => 12 111101001000 => 12 111101010000 => 12 111101100000 => 12 111110000010 => 12 111110000100 => 12 111110001000 => 12 111110010000 => 12 111110100000 => 12 111111000000 => 12 100001111100 => 7 10110111100000 => 9 10111011010000 => 11 10111011100000 => 10 10111100110000 => 10 10111101001000 => 11 10111101010000 => 11 10111101100000 => 10 10111110000100 => 10 10111110001000 => 10 10111110010000 => 10 10111110100000 => 10 10111111000000 => 9 11001111100000 => 11 11011110000010 => 12 11101101000010 => 14 11101110000010 => 14 11110011000010 => 14 11110100100010 => 14 11110101000010 => 14 11110110000010 => 14 11111000001100 => 14 11111000010010 => 14 11111000100010 => 14 11111001000010 => 14 11111010000010 => 14 11111100000010 => 14 1011110111000000 => 11 1011111010100000 => 12 1011111011000000 => 11 1011111100010000 => 11 1011111100100000 => 11 1011111101000000 => 11 1011111110000000 => 10 1111011100000010 => 16 1111101010000010 => 16 1111101100000010 => 16 1111110001000010 => 16 1111110010000010 => 16 1111110100000010 => 16 1111111000000010 => 16 ----------------------------------------------------------------------------- Created: Jul 02, 2019 at 11:52 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Jul 04, 2019 at 22:29 by Martin Rubey