A247202 Smallest odd k > 1 such that k*2^n - 1 is a prime number.

3, 3, 3, 3, 7, 3, 3, 5, 7, 5, 3, 5, 9, 5, 9, 17, 7, 3, 51, 17, 7, 33, 13, 39, 57, 11, 21, 27, 7, 213, 15, 5, 31, 3, 25, 17, 21, 3, 25, 107, 15, 33, 3, 35, 7, 23, 31, 5, 19, 11, 21, 65, 147, 5, 3, 33, 51, 77, 45, 17, 69, 53, 9, 3, 67, 63, 43, 63, 51, 27, 73, 5

Offset

1,1

Comments

Limit_{N->oo} (Sum_{n=1..N} a(n))/(Sum_{n=1..N} n) = log(2). [[Is there a proof or is this a conjecture? - Peter Luschny, Feb 06 2015]]

Records: 3, 7, 9, 17, 51, 57, 213, 255, 267, 321, 615, 651, 867, 901, 909, 1001, 1255, 1729, 1905, 2163, 3003, 3007, 3515, 3797, 3825, 4261, 4335, 5425, 5717, 6233, 6525, 6763, 11413, 11919, 12935, 20475, 20869, 25845, 30695, 31039, 31309, 42991, 55999, ... . - Robert G. Wilson v, Feb 08 2015

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..10031 (first 5000 terms from Pierre CAMI)

Formula

a(A002235(n)) = 3.

Maple

f:= proc(n)
local k, p;
  p:= 2^n;
for k from 3 by 2 do if isprime(k*p-1) then return k fi od;
end proc:
seq(f(n), n=1 .. 100); # Robert Israel, Feb 05 2015

Mathematica

f[n_] := Block[{k = 3, p = 2^n}, While[ !PrimeQ[k*p - 1], k += 2]; k]; Array[f, 70]

Prog

(PFGW & SCRIPT)
SCRIPT
DIM k
DIM n, 0
DIMS t
OPENFILEOUT myf, a(n).txt
LABEL loop1
SET n, n+1
SET k, 1
LABEL loop2
SET k, k+2
SETS t, %d, %d\,; n; k
PRP k*2^n-1, t
IF ISPRP THEN GOTO a
GOTO loop2
LABEL a
WRITE myf, t
GOTO loop1
(PARI) a(n) = {k=3; while (!isprime(k*2^n-1), k+=2); k; } \\ Michel Marcus, Nov 25 2014

Crossrefs

Cf. A126715, A247479.

Sequence in context: A263137 A320846 A277515 * A195758 A304684 A079084

Adjacent sequences: A247199 A247200 A247201 * A247203 A247204 A247205

Keyword

nonn

Author

Pierre CAMI, Nov 25 2014

Status

approved