A139426 Smallest number k such that M(n)^2+k*M(n)-1 is prime with M(n)= Mersenne primes =A000668(n).

1, 5, 1, 5, 11, 11, 17, 19, 23, 97, 127, 145, 167, 269, 767, 479, 3307, 1453, 18007, 2357, 599, 17669, 5527, 3191, 3251, 70249, 147773, 39637

Offset: 1

Author

Pierre CAMI, Apr 21 2008

Keywords

• hard
• more
• nonn

Comments

All primes certified using openpfgw_v12 from primeform group.

Examples

			3*3+1*3-1=11 prime 3=M(1)=2^2-1 so k(1)=1;
7*7+5*7-1=83 prime 7=M(2)=2^3-1 so k(2)=5;
31*31+1*31-1=991 prime 31=M(3)=2^5-1 so k(3)=1.
		

Crossrefs

Cf. A000668, A139424, A139425, A139427, A139428, A139429, A139430, A139421, A143385.

Programs

Mathematica

A000043 = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609};
Table[m = 2^A000043[[n]] - 1; m2 = m^2; k = 1;
While[! PrimeQ[m2 + k*m - 1], k++]; k, {n, 15}] (* Robert Price, Apr 17 2019 *)

Extensions

3 more terms. - Pierre CAMI, Aug 11 2008