

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
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OFFSET

1,1


LINKS



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



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



