A249806 Smallest odd number k>1 such that k*2^prime(n)-1 is also prime.

3, 3, 7, 3, 3, 9, 7, 51, 13, 7, 15, 21, 15, 3, 31, 147, 45, 69, 43, 73, 15, 69, 91, 19, 51, 81, 3, 25, 9, 85, 103, 55, 169, 225, 109, 145, 15, 103, 615, 69, 259, 69, 63, 45, 285, 471, 9, 255, 169, 489, 69, 273, 427, 43, 391, 169, 201, 21

Offset: 1

Author

Pierre CAMI, Nov 06 2014

Keywords

• nonn

Comments

If prime(n) is a Mersenne prime exponent then 2^prime(n)-1 is a prime < k*2^prime(n)-1.

Links

• Pierre CAMI, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A135434.

Programs

Maple

3*2^2-1=11 prime so a(1)=3.
3*2^3-1=23 prime so a(2)=3.
3*2^5-1=95 composite, 5*2^5-1=159 composite, 7*2^5-1=223 prime so a(3)=7.

Mathematica

a249806[n_Integer] := Catch[Module[{k}, For[k = 3, k < 10^5, k += 2, If[PrimeQ[k*2^Prime[n] - 1], Throw[k], 0]]]]; a249806 /@ Range[120] (* Michael De Vlieger, Nov 11 2014 *)

PARI

s=[]; forprime(p=2, 500, k=3; q=2^p; while(!ispseudoprime(k*q-1), k+=2); s=concat(s, k)); s \\ Colin Barker, Nov 06 2014