A261414 2^n+1 appears in A109732 at position a(n).

2, 5, 30, 38, 201, 242, 689, 1806, 7175, 10839, 21474, 64607, 290563, 290579, 581260, 872576, 2617577, 5238258, 7858320, 19886365, 47140605, 70713773, 212133736

Offset

1,1

Comments

This assumes van der Poorten's conjecture that every odd number does appear in A109732.

Links

Table of n, a(n) for n=1..23.

Example

A109732(38) = 17 = 2^4+1, so a(4)=38.

Maple

m:= 22000: # m is the search limit
b:= proc() true end:
s:= heap[new]((x, y)-> is(x>y), 1):
for n to m do t:= heap[extract](s); b(t):= false;
  if t>1 and t-1=2^ilog2(t-1) then print(ilog2(t-1), t, n) fi;
  k:= 2*t+1; if b(k) then heap[insert](k, s) fi;
  if irem(t, 3, 'k')=0 and b(k) then heap[insert](k, s) fi
od:  # Alois P. Heinz, Aug 27 2015

Mathematica

maxVal = 5*10^5; (* 5*10^5 gives 12 terms *)
f[n_] := Module[{lst = {}, x = n}, While[x = 2x+1; x < maxVal, AppendTo[lst, x]]; lst];
M = {1}; pending = f[1];
A261414 = Reap[Print[2]; Sow[2]; While[Length[pending] > 0, next = First[pending]; pending = Rest[pending]; If[!MemberQ[M, next], AppendTo[M, next]; While[Mod[next, 3]==0 && !MemberQ[M, next/3], next = next/3; If[IntegerQ[Log[2, next-1]], Print[an = Length[M]+1]; Sow[an]]; AppendTo[M, next]; pending = Union[pending, f[next]]]]]][[2, 1]] (* Jean-François Alcover, Nov 25 2020, after T. D. Noe in A109732 *)

Crossrefs

Cf. A109732, A109734, A109739, A109740, A261412, A261413.

Sequence in context: A158866 A101078 A109739 * A163800 A180826 A367521

Adjacent sequences: A261411 A261412 A261413 * A261415 A261416 A261417

Keyword

nonn,more

Author

N. J. A. Sloane, Aug 25 2015

Extensions

a(10)-a(17) from Alois P. Heinz, Aug 27 2015

a(18)-a(23) from Alois P. Heinz, Aug 28 2015

Status

approved