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

1,1

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.

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A355793 A173424 A143081 * A112811 A197272 A306773

Adjacent sequences: A179655 A179656 A179657 * A179659 A179660 A179661

Keyword

nonn

Author

Karsten Bonath, Jul 23 2010

Extensions

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

Status

approved