A258823 Numbers n such that k iterations of n under the '3x+1' map yield k for some k.

2, 7, 8, 10, 18, 19, 24, 26, 41, 43, 44, 45, 46, 48, 52, 53, 64, 65, 66, 67, 72, 74, 76, 77, 97, 98, 99, 100, 101, 102, 112, 116, 117, 120, 122, 144, 148, 149, 153, 156, 157, 158, 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

Offset

1,1

Comments

Numbers n such that A258822(n) > 0.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

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.
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.

Mathematica

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 *)

Prog

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

Crossrefs

Cf. A258822, A006370, A070165.

Sequence in context: A356671 A047525 A075766 * A226612 A005538 A329648

Adjacent sequences: A258820 A258821 A258822 * A258824 A258825 A258826

Keyword

nonn

Author

Derek Orr, Jun 11 2015

Status

approved