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
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
KEYWORD
nonn,more
AUTHOR
Dmitry Kamenetsky, Oct 26 2016
EXTENSIONS
Duplicated term 300 removed by Hartmut F. W. Hoft, Aug 16 2018
STATUS
approved