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A226614 Positive integers k for which 1 is in a cycle of integers under iteration by the Collatz-like 3x+k function.

%I A226614 #11 Aug 05 2013 07:47:53
%S A226614 1,5,11,13,17,29,41,43,55,59,61,77,79,91,95,97,107,113,119,125,127,
%T A226614 137,145,155,185,193,203,209,215,239,247,253,257,275,281,289,317,329,
%U A226614 335,353,355,407,437,445,473,493,499,509,553,559,593,629,637,643,673,697
%N A226614 Positive integers k for which 1 is in a cycle of integers under iteration by the Collatz-like 3x+k function.
%C A226614 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. GCD(k,6)=1.
%C A226614 When k=2^m-3, T_k has a cycle containing 1. Hence the sequence is infinite.
%C A226614 a(n) is in the sequence if and only if A226607(A226612(floor(a(n)/3)+1)) = 1.
%C A226614 Trivially, members of the sequence are not divisible by 2 or 3. Of the first 10^4 members, only 1,066 are squareful, which is about one third of the expected density. - _Ralf Stephan_, Aug 05 2013
%H A226614 Geoffrey H. Morley, <a href="/A226614/b226614.txt">Table of n, a(n) for n = 1..10000</a>
%H A226614 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%o A226614 (PARI) \\ 5.5 hours (2.33 Ghz Intel Core 2)
%o A226614 {k=1; n=1;
%o A226614 until(n>10000, x=1; y=1; len=0;
%o A226614   until(x==y, if(x%2==0, x=x/2, x=(3*x+k)/2);
%o A226614     if(y%2==0, y=y/2, y=(3*y+k)/2);
%o A226614     if(y%2==0, y=y/2, y=(3*y+k)/2); len++);
%o A226614   if(x==1, write("b226614.txt",n," ",k);
%o A226614     write("b226615.txt",n," ",len); n++);
%o A226614   k+=(k+3)%6)}
%Y A226614 Cf. A226615-A226618.
%K A226614 nonn
%O A226614 1,2
%A A226614 _Geoffrey H. Morley_, Aug 02 2013