%I #6 Jan 13 2017 10:41:16

%S 2,7,8,10,18,19,24,26,41,43,44,45,46,48,52,53,64,65,66,67,72,74,76,77,

%T 97,98,99,100,101,102,112,116,117,120,122,144,148,149,153,156,157,158,

%U 160,172,173,174,175,209,210,211,246,247,248,249,250,252,253,254,255,260,261,262,264,266,268,269,272

%N Numbers n such that k iterations of n under the '3x+1' map yield k for some k.

%C Numbers n such that A258822(n) > 0.

%H Harvey P. Dale, <a href="/A258823/b258823.txt">Table of n, a(n) for n = 1..1000</a>

%e For n = 6, the '3x+1' map is as follows: 6 -> 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1. For any possible k, after the k-th iteration, the result does not equal k. Thus 6 is not a member of this sequence.

%e For n = 7, the '3x+1' map is as follows: 7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1. After 10 iterations, we arrive at 10. So, 7 is a member of this sequence.

%t kQ[n_]:=Module[{tr=Rest[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n, #>1&]], len}, len = Length[ tr];Count[Thread[{tr,Range[len]}],_?(#[[1]] == #[[2]]&)]>0]; Select[Range[300],kQ] (* _Harvey P. Dale_, Jan 13 2017 *)

%o (PARI) Tvect(n)=v=[n]; while(n!=1, if(n%2, k=3*n+1; v=concat(v, k); n=k); if(!(n%2), k=n/2; v=concat(v, k); n=k)); v

%o n=1;while(n<10^3,d=Tvect(n); c=0; for(i=1, #d, if(d[i]==i-1,print1(n, ", ");break));n++)

%Y Cf. A258822, A006370, A070165.

%K nonn

%O 1,1

%A _Derek Orr_, Jun 11 2015