A070917 Numbers n such that the number of steps to reach 1 in the "3x+1" (or Collatz) problem divides n.

2, 4, 5, 16, 21, 40, 70, 96, 100, 120, 150, 160, 170, 180, 208, 238, 256, 261, 272, 288, 341, 405, 485, 544, 625, 650, 672, 693, 720, 756, 767, 784, 868, 966, 1005, 1078, 1248, 1271, 1300, 1326, 1352, 1365, 1428, 1430, 1536, 1638, 1664, 1680, 1696, 1740

Offset

1,1

Links

Table of n, a(n) for n=1..50.

Example

The trajectory of 21 under the "3x+1" map is : 21 ->64 ->32 ->16 ->8 ->4 ->2 ->1 So 7 steps are needing to reach 1 and 7 divides 21, hence 21 is in the sequence. For 261, 29 steps are needing and 261/29=9 hence 261 is also in the sequence.

Mathematica

nsdnQ[n_]:=Divisible[n, Length[NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&]]-1]; Select[Range[2, 1800], nsdnQ] (* Harvey P. Dale, Mar 24 2018 *)

Prog

(PARI) for(n=2, 3000, s=n; t=0; while(s!=1, t++; if(s%2==0, s=s/2, s=3*s+1); if(s==1+n*frac(n/t), print1(n, ", "); ); ))

Crossrefs

Sequence in context: A056401 A056406 A250545 * A038757 A377142 A062549

Adjacent sequences: A070914 A070915 A070916 * A070918 A070919 A070920

Keyword

easy,nonn

Author

Benoit Cloitre, May 20 2002

Status

approved