A139427 Smallest number k such that M(n)^2+k*M(n)+1 is prime with M(n)= Mersenne primes =A000668(n).

1, 3, 5, 17, 17, 5, 83, 63, 71, 101, 543, 59, 569, 1029, 353, 1851, 2801, 2619, 525, 2907, 8955, 437, 30159, 5409, 8355

Offset

1,2

Comments

All primes certified using openpfgw_v12 from primeform group

Links

Table of n, a(n) for n=1..25.

Example

3*3+1*3+1=13 prime 3=M(1)=2^2-1 so k(1)=1;
7*7+3*7+1=71 prime 7=M(2)=2^3-1 so k(2)=3;
31*31+5*31+1=1117 prime 31=M(3)=2^5-1 so k(3)=5.

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 *)

Crossrefs

Cf. A000668, A139424, A139425, A139426, A139428, A139429, A139430, A139421.

Sequence in context: A339944 A359395 A292008 * A360802 A365475 A191051

Adjacent sequences: A139424 A139425 A139426 * A139428 A139429 A139430

Keyword

hard,more,nonn

Author

Pierre CAMI, Apr 21 2008

Status

approved