A238694 Smallest k such that 2^n - k and k*2^n - 1 are both prime or 0 if no such k exists.

0, 1, 1, 3, 1, 3, 1, 5, 25, 5, 31, 5, 1, 15, 49, 17, 1, 5, 1, 17, 9, 33, 69, 89, 61, 111, 199, 309, 75, 297, 1, 5, 49, 131, 31, 17, 31, 131, 165, 437, 55, 33, 309, 495, 361, 437, 999, 89, 139, 195, 129, 183, 685, 315, 915, 189, 585, 1035, 931, 93, 1, 57, 165

Offset: 1

Author

Ilya Lopatin and Juri-Stepan Gerasimov, Mar 03 2014

Keywords

• nonn

Comments

If a(n)=1, then the two primes are same and they are Mersenne primes (A000668).

Examples

			a(9) = 25 because 2^9 - 25  = 487 and 25*2^9 - 1 = 12799 are both prime.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A238554.

Programs

Maple

a:= proc(n) local k, p; p:= 2^n;
      for k while not (isprime(p-k) and isprime(k*p-1))
        do if k>=p then return 0 fi od; k
    end:
seq(a(n), n=1..70);  # Alois P. Heinz, Mar 03 2014

Mathematica

a[n_] := Module[{k, p}, p = 2^n;
     For[k = 1, !(PrimeQ[p - k] && PrimeQ[k*p - 1]), k++,
           If[k >= p, Return[0]]]; k];
Table[a[n], {n, 1, 70}] (* Jean-François Alcover, Feb 18 2022, after Alois P. Heinz *)

Extensions

More terms from Alois P. Heinz, Mar 03 2014