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A226665 Conjectured record-breaking maximal values, for ascending positive integers k, of the minimal elements of the primitive cycles of positive integers under iteration by the Collatz-like 3x+k function.

%I A226665 #10 Jul 04 2013 21:12:10
%S A226665 1,347,7055,177337,212665,219913,379541,413803,822535,1391321,8013899,
%T A226665 21619279,21834347,28306063,37550317,168536521,189763177
%N A226665 Conjectured record-breaking maximal values, for ascending positive integers k, of the minimal elements of the primitive cycles of positive integers under iteration by the Collatz-like 3x+k function.
%C A226665 A cycle is called primitive if its elements are not a common multiple of the elements of another cycle.
%C A226665 The 3x+k function T_k is defined by T_k(x) = x/2 if x is even, (3x+k)/2 if x is odd, where k is odd.
%C A226665 For primitive cycles, GCD(k,6)=1.
%e A226665 a(1)=1 because {1,2}, with minimal element 1, is the only known '3x+1' cycle of positive integers.
%e A226665 k=5 is the next value of k>1 with GCD(k,6)=1. The minimal element in each of the five known primitive '3x+5' cycles of positive integers is 1, 19, 23, 187 and 347. 347>a(1) so a(2)=347.
%Y A226665 k = A226666(n).
%Y A226665 Cf. A226607, A226681.
%K A226665 nonn
%O A226665 1,2
%A A226665 _Geoffrey H. Morley_, Jun 16 2013