%I #11 Aug 22 2024 20:52:09
%S 1,3,7,8,11,13,14,18,24,26,27,29,32,33,36,37,39,40,43,45,46,51,52,56,
%T 57,61,62,63,65,66,85,86,87,94,100,101,103,105,106,107,109,111,113,
%U 114,115,121,130,131,136,141,142,145,146,147,153,155,158,164,166,167,168,169
%N First cycle is reached under a "Collatz-Fibonacci" transform (cf. comment).
%C Let x(1)=1 x(2)=n; x(k)=x(k-1)+x(k-2) if x(k-1) and x(k-2) have opposite parities; x(k)=abs(x(k-1)-x(k-2))/2 otherwise. Conjecture : for any n x(k) reaches a cycle among 2 cycles : (1;1;0) and (1;2;3;5). Sequence gives values of n such that (1;1;0) is reached.
%F a(n)/n seems greater than 2 for n large enough and if limit a(n)/n exists, this limit should be > 2.5. Does a(n)/n = O(log(log(n)))?
%K nonn
%O 1,2
%A _Benoit Cloitre_, Jan 02 2003