WON plate123 | World!OfNumbers [ January 22, 2002 ]John McNamara brings democracy into the Rabbit series. Take the Rabbit series set out in Fibonacci length substrings 1 0 11 010 11011 01011010 1101101011011 010110101101101011010 1101101011011010110101101101011011 It is undemocratic! There are more ones than zeros, (1.618034 ones to 1 zeros approx.) This is rectified by using its undemocratic self modified to rectify the situation. The "modified" series used was 01011010... in other words, the normal Rabbit sequence with 0 tacked on the beginning which is why the first "cut" is three bits and not 5. So taking three bits for a 0, and five bits for a 1 and operating on the original series using the modified series, we get (using asterisks as separators), and we"or" every second string, (i.e. swap a 0 for a 1 and vice versa): 1 0 1*1 010 1*101*1 0101*1010 1*101*10101*101*1 0101*10101*101*10101*1010 1*101*10101*101*10101*10101*101*10101*101*1 etc. (incidentally showing a marvellous symmetry) So we have 101*10101*101*10101*10101*101*10101*101*1 etc. which, if "or"ed after one asterisk and un"or"ed after the next asterisk etc. becomes 101*01010*101*01010*10101*010*10101*010*1 etc., which IS democratic. Source : mistermac See also related WONplate 118 A000123 Prime Curios! Prime Puzzle Wikipedia 123 Le nombre 123
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