A277684 Least k such that A277109(k) = 2^n - 1.

0, 6, 17, 18, 69, 70, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 464, 465, 466, 467, 624, 625, 1810, 1811, 1812

Offset

1,2

Comments

Are the terms always increasing? Note, if the conjecture in A277109 is true then the terms in this sequence are guaranteed to be increasing.

Since the conjecture in A277109 is true, this sequence is strictly increasing. - Hartmut F. W. Hoft, Aug 16 2018

Links

Table of n, a(n) for n=1..26.

Example

Since A277109(69) = 15 is the first occurrence of 15 = 2^4 - 1, a(4) = 69. - Hartmut F. W. Hoft, Aug 16 2018

Mathematica

collatzN[n_] := Length[NestWhileList[If[EvenQ[#], #/2, 3# + 1]&, n, #!=1&]]
collatzNrun[n_] := Module[{run=collatzN[n], k=1}, While[collatzN[n+k]==run, k++]; k]
power2[k_] := Module[{list=NestWhileList[#/2&, k, EvenQ]}, {Last[list], Length[list]-1}]
(* a277684[] computes all values through index n *)
a277684[n_] := Module[{i, list={0}}, For[i=1, i<=n, i++, If[power2[collatzNrun[2^i+1]+1] == {1, Length[list]+1}, AppendTo[list, i]]]; list]/; n>0 (* Hartmut F. W. Hoft, Aug 16 2018 *)

Prog

(PARI) nbsteps(n)= s=n; c=0; while(s>1, s=if(s%2, 3*s+1, s/2); c++); c;
len(n) = {my(ns = 2^n+1); my(nbs = nbsteps(ns)); while(nbsteps(ns+1) == nbs, ns++); ns - 2^n; }
a(n) = {k=0; while(len(k) != 2^n-1, k++); k; } \\ Michel Marcus, Oct 30 2016

Crossrefs

Cf. A277109.

Sequence in context: A063584 A019296 A035484 * A009171 A012417 A184549

Adjacent sequences: A277681 A277682 A277683 * A277685 A277686 A277687

Keyword

nonn,more

Author

Dmitry Kamenetsky, Oct 26 2016

Extensions

Duplicated term 300 removed by Hartmut F. W. Hoft, Aug 16 2018

Status

approved