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%I #11 Jul 10 2015 19:25:56
%S 12334444,111,117,1223,78,111177,11127,11144445,11667,1111113
%N Except for the first term the number in the sequence is the smallest number in a new cycle of a RATS sequence with a new destiny. The first term is the best analog of this for the "infinite cycle".
%C "Destiny" means the smallest element of the cycle that the trajectory ends up in.
%C All seeds except those generating the cycles listed here produce an open non-cyclic family (thus without lowest element) but with a regular structure like 12334444, 55667777, 123334444, 556667777, 1233334444, 5566667777,..., and with an arbitrary start-up like 1, 2, 4, 8, 16, 77, 145, 668, 1345, 6677, 13444, 55778, 133345, 666677, 1333444, 5567777, 12333445, 66666677, 133333444, 556667777, 1233334444, 5566667777, 12333334444, 55666667777, 123333334444, ... Notice that here we fall into the regular regime starting with 1233334444 (four threes. The sequence gives 12-(two threes)-4444 as a representative with index 1. - _Wouter Meeussen_, Jul 26 2009
%H Tanya Khovanova, <a href="http://blog.tanyakhovanova.com/?p=155">Destinies of Numbers</a> - _Tanya Khovanova_, Aug 10 2009
%Y Cf. A004000, A036839, A066710, A066711, A161590.
%Y Cf. A161593, A161596. - _Tanya Khovanova_, Aug 10 2009
%K nonn,base
%O 1,1
%A _J. H. Conway_ & _Tanya Khovanova_, Jun 14 2009
%E 11667, 1111113 from _Wouter Meeussen_, Jul 04 2009
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