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
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.
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
Comments