[seqfan] Self-describing the divisibility by 5

[Eric Angelini]

Hello SeqFans,

F=
1,5,2,3,4,6,7,50,8,51,10,52,9,11,500,12,13,53,14,20,16,54,17,18,19,21,30,22,23,24,26,27,28,29,40,31,32,33,34,36,37,38,39,41,42,43,151,44,46,47,152,48,49,61,62,63,64,66,67,68,69,71,72,73,74,76,77,78,79,81,82,83,84,86,87,88,56,89,91,92,93,153,94,96,97,60,98,99,101,102,103,104,106,107,70,108,109,111,112,113,114,154,116,117,1051,118,119,121,156,122,123,124,126,127,128,129,131,132,133,134,136,137,138,139,141,142,143,144,146,147,148,149,161,162,163,164,166,167,168,169,171,172,173,174,176,177,80,178,179,181,182,183,184,186,187,188,189,90,191,192,193,194,196,197,198,199,201,...

Mark in blue the integers divisible by 5;
the non-blue integers appear in chunks
whose successive sizes are given by F itself.

Forget the blue color now and mark  
in yellow all the "5" of F;
the non-yellow digits appear in chunks
whose successive sizes are given by 
F itself.

I've chosen the "divisible-by-5" rule
because kids can very easely follow
the above instructions -- and be amazed.
But "divisible-by-7" could be computed, of course, or "divisible-by-666" (in this case you'll yellow 
all the 666 substrings).

F is the lexico-first such seq (and not
the Mexico-first as suggested by the 
autocorrect) and F is _not_ a permutation
of the Naturals (55, 155, 255, ... will 
never show, for instance, as the zero
gap between two consecutive 5 would
produce a zero in F).

Best,
É.