A226614 - OEIS

%I #11 Aug 05 2013 07:47:53

%S 1,5,11,13,17,29,41,43,55,59,61,77,79,91,95,97,107,113,119,125,127,

%T 137,145,155,185,193,203,209,215,239,247,253,257,275,281,289,317,329,

%U 335,353,355,407,437,445,473,493,499,509,553,559,593,629,637,643,673,697

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

%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. GCD(k,6)=1.

%C When k=2^m-3, T_k has a cycle containing 1. Hence the sequence is infinite.

%C a(n) is in the sequence if and only if A226607(A226612(floor(a(n)/3)+1)) = 1.

%C 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 Geoffrey H. Morley, <a href="/A226614/b226614.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%o (PARI) \\ 5.5 hours (2.33 Ghz Intel Core 2)

%o {k=1; n=1;

%o until(n>10000, x=1; y=1; len=0;

%o   until(x==y, if(x%2==0, x=x/2, x=(3*x+k)/2);

%o     if(y%2==0, y=y/2, y=(3*y+k)/2);

%o     if(y%2==0, y=y/2, y=(3*y+k)/2); len++);

%o   if(x==1, write("b226614.txt",n," ",k);

%o     write("b226615.txt",n," ",len); n++);

%o   k+=(k+3)%6)}

%Y Cf. A226615-A226618.

%K nonn

%O 1,2

%A _Geoffrey H. Morley_, Aug 02 2013