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A226686 Conjectured record-breaking lengths, for ascending positive integers k, of primitive cycles of positive integers under iteration by the Collatz-like 3x-k function. 5

%I #8 Jun 18 2013 12:36:01

%S 11,17,19,34,69,84,85,168,171,176,179,228,252,285

%N Conjectured record-breaking lengths, for ascending positive integers k, of primitive cycles of positive integers under iteration by the Collatz-like 3x-k function.

%C A cycle is called primitive if its elements are not a common multiple of the elements of another cycle.

%C 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.

%C For primitive cycles, GCD(k,6)=1.

%Y k = A226687(n). The smallest integer in the T_k cycle(s) associated with a(n) is A226688(n).

%Y Cf. A226625, A226670.

%K nonn

%O 1,1

%A _Geoffrey H. Morley_, Jun 16 2013

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