A109739 -id:A109739 - cp's OEIS frontend

A109734 In A109732, the number 2n+1 appears in position a(n).

1, 2, 5, 3, 30, 6, 28, 4, 38, 26, 11, 7, 36, 29, 14, 8, 201, 39, 34, 27, 180, 12, 175, 9, 199, 37, 46, 31, 25, 15, 178, 10, 242, 202, 49, 40, 197, 35, 54, 32, 192, 158, 23, 13, 208, 176, 57, 16, 240, 200, 61, 41, 83, 47, 195, 33, 121, 42, 67, 17, 190, 179, 70, 18, 689, 243

Offset: 0

N. J. A. Sloane, Aug 10 2005

nonn

			9 appears in position 30 in A109732, so a(4) = 30.

N. J. A. Sloane and Alois P. Heinz, Table of n, a(n) for n = 0..20000 (first 1024 terms from N. J. A. Sloane)

Cf. A109732. For records see A109739 and A109740.

with(LinearAlgebra);
hit:=Array(1..200000); a:=[1,3,7];
hit[1]:=1; hit[3]:=2; hit[7]:=3; S:={15}; L:=7;
for n from 4 to 20000 do
if (L mod 3 = 0) and hit[L/3]=0 then
L:=L/3; a:=[op(a),L]; hit[L]:=n; S:= S minus {L};
   if hit[2*L+1]=0 then S:=S union {2*L+1}; fi;
else L:=min(S); a:=[op(a),L]; hit[L]:=n; S:=S minus {L};
   if hit[2*L+1]=0 then S:=S union {2*L+1}; fi;
fi;
od:
#a;
w:=[];
for i from 0 to 50000 do
if hit[2*i+1]=0 then break; fi;
w:=[op(w),hit[2*i+1]]; od:
w; # N. J. A. Sloane, Aug 25 2015

(* using the M generated in A109732 *) ms=Sort[M]; k=1; While[ms[[k]]==2k-1, k++ ]; k=k-1; Take[Ordering[M], k] (* T. D. Noe, Aug 10 2005 *)

More terms from T. D. Noe and Ray Chandler, Aug 10 2005

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

Original entry on oeis.org

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

N. J. A. Sloane, Aug 25 2015

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

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

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

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

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 *)

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

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

cp's OEIS Frontend

A109734 In A109732, the number 2n+1 appears in position a(n).

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