A346139 Numbers k that require fewer than k steps to reach 1 under the 3x+1 map.

1, 2, 4, 8, 10, 12, 13, 16, 17, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 61, 64, 65, 66, 67, 68, 69, 70, 72, 74, 75, 76, 77, 78, 79, 80, 81, 84, 85, 86, 87, 88

Offset

1,2

Comments

Numbers k such that A006577(k) < k.

Is 5 the only positive number neither in this sequence, nor in A228014 (cf. Caldwell, Honaker)?

Links

Table of n, a(n) for n=1..66.

Chris K. Caldwell and G. L. Honaker, Jr., Curio for 5

Index entries for sequences related to 3x+1 (or Collatz) problem

Example

The trajectory of 13 under repeated applications of the Collatz map starts 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, requiring 9 steps to reach 1. 9 < 13, so 13 is a term of the sequence.

Mathematica

nsteps[n_] := -1 + Length @ NestWhileList[If[OddQ[#], 3 # + 1, #/2] &, n, # > 1 &]; Select[Range[100], nsteps[#] < # &] (* Amiram Eldar, Jul 14 2021 *)

Prog

(PARI) a006370(n) = if(n%2==0, n/2, 3*n+1)
is(n) = my(x=n, i=0); while(1, if(x==1, if(i < n, return(1), return(0))); x=a006370(x); i++)

Crossrefs

Cf. A006370, A006577, A082984, A228014.

Sequence in context: A174567 A178330 A029992 * A206928 A133012 A039011

Adjacent sequences: A346136 A346137 A346138 * A346140 A346141 A346142

Keyword

nonn

Author

Felix Fröhlich, Jul 14 2021

Status

approved