A253398 -id:A253398 - cp's OEIS frontend

A247479 Smallest odd k > 1 such that k*2^n+1 is a prime number.

3, 3, 5, 7, 3, 3, 5, 3, 15, 13, 9, 3, 5, 7, 5, 21, 9, 3, 11, 7, 11, 25, 45, 45, 5, 7, 15, 13, 23, 3, 35, 43, 9, 75, 59, 3, 15, 15, 5, 27, 3, 9, 9, 15, 35, 19, 27, 15, 23, 7, 17, 7, 51, 49, 5, 27, 29, 99, 27, 31, 53, 105, 9, 25, 9, 3, 9, 31, 23

Offset: 1

Pierre CAMI, Dec 01 2014

nonn

Differs from A057778 only where n is related to a Fermat prime (A019434). - R. J. Mathar, Dec 02 2014

Records: 3, 5, 7, 15, 21, 25, 45, 75, 99, 105, 127, 249, 321, 363, 411, 421, 535, 823, 1383, 1875, 2375, 2443, 2865, 4063, 4141, 4239, 4623, 5175, 5469, 14319, 15979, 17817, 25925, 30487, 39741, 48055, 49709, 50721, 55367, ... . - Robert G. Wilson v, Feb 02 2015

Robert G. Wilson v, Table of n, a(n) for n = 1..10111 (first 5150 terms from Pierre CAMI)

Cf. A035050, A057778, A247202, A253398.

A247479:= proc(n) local k;
      for k from 3 by 2 do if isprime(k*2^n+1) then return k fi od
   end proc:
seq(A247479(n),n=1..100); # Robert Israel, Dec 01 2014

f[n_] := Block[{k = 3, p = 2^n}, While[ !PrimeQ[k*p + 1], k += 2]; k]; Array[f, 70] (* Robert G. Wilson v, Jan 29 2015 *)

a(n) = {k = 3; while (! isprime(k*2^n+1), k += 2); k;} \\ Michel Marcus, Dec 01 2014

A361546 a(n) is the least odd number k such that k*2^prime(n) + 1 is prime, or -1 if no such number k exists.

Original entry on oeis.org

1, 5, 3, 5, 9, 5, 9, 11, 45, 23, 35, 15, 3, 9, 27, 51, 27, 53, 9, 39, 23, 249, 51, 51, 131, 221, 29, 105, 321, 179, 5, 221, 111, 411, 191, 65, 83, 75, 95, 101, 147, 83, 149, 111, 203, 131, 9, 245, 281, 15, 83, 65, 299, 39, 51, 51, 225, 65, 81, 125, 611, 143, 65, 107, 21

Offset: 1

Jean-Marc Rebert, Mar 15 2023

nonn

			prime(1) = 2 and 1*2^2 + 1 = 5 is prime, and no lesser odd k satisfies this, so a(1) = 1.

Jean-Marc Rebert, Table of n, a(n) for n = 1..1000

Cf. A076336. Essentially the same as A253398.

a[n_] := Module[{m = 2^Prime[n], k = 1}, While[!PrimeQ[k*m + 1], k += 2]; k]; Array[a, 65] (* Amiram Eldar, Mar 15 2023 *)

a(n)=my(m=2^prime(n),k=1);while(!isprime(k*m+1),k+=2);k

cp's OEIS Frontend

A247479 Smallest odd k > 1 such that k*2^n+1 is a prime number.

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