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[ 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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