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A070917 Numbers n such that the number of steps to reach 1 in the "3x+1" (or Collatz) problem divides n. 0
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 (list; graph; refs; listen; history; text; internal format)
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 A062549 A169602

Adjacent sequences:  A070914 A070915 A070916 * A070918 A070919 A070920

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, May 20 2002

STATUS

approved

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Last modified November 17 13:33 EST 2019. Contains 329230 sequences. (Running on oeis4.)