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

Author

Dmitry Kamenetsky, Oct 26 2016

Keywords

• nonn
• more

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

Examples

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

Crossrefs

Cf. A277109.

Programs

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 *)

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

Extensions

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