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

Author

N. J. A. Sloane, Aug 25 2015

Keywords

• nonn
• more

Comments

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

Examples

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

Crossrefs

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

Programs

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 *)

Extensions

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

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