A179658 Minimal odd k such that k*2^n-1 and k*2^(n+1)-1 are Sophie Germain primes.

3, 1, 3, 15, 45, 3, 99, 45, 51, 141, 153, 177, 411, 45, 45, 267, 237, 75, 75, 207, 111, 111, 123, 159, 57, 375, 1419, 45, 291, 321, 489, 585, 525, 1623, 579, 45, 27, 1293, 1059, 255, 2265, 33, 465, 165, 405, 315, 315, 117, 411, 1725, 2343, 2397, 465, 315, 1443

Offset: 1

Author

Karsten Bonath, Jul 23 2010

Keywords

• nonn
• changed

Comments

In the b-file up to n=10000, only a(2) is not a multiple of 3 and all entries are odd, so heuristically a(n) = A176248(n) for n>2. - R. J. Mathar, Aug 28 2025

Examples

			Example for n=7: a(7)=99 because 99*2^7-1 and 99*2^8-1 is the first occurrence for n=7 as a Sophie Germain prime pair.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (from Bonath's link)
• Karsten Bonath, First odd k for which k * 2^n - 1 and k * 2^(n + 1) - 1 are prime.

Crossrefs

Cf. A005384, A076806 (minimal odd k such that k*2^n-1 and k*2^n+1 are twin primes).

Programs

Magma

a:=[]; for n in [1..55] do k:=1; while not (IsPrime(k*2^n-1) and IsPrime(k*2^(n+1)-1)) do k:=k+2; end while; Append(~a,k); end for; a; // Marius A. Burtea, Jan 16 2020

Mathematica

a[n_] := Module[{k = 1}, While[!And @@ PrimeQ[k * 2^{n, n+1} - 1], k += 2]; k]; Array[a, 30] (* Amiram Eldar, Jan 16 2020 *)

Extensions

More terms from Bonath's link added by Amiram Eldar, Jan 16 2020