A139428 - OEIS

A139428

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

5, 7, 5, 17, 43, 67, 41, 53, 311, 317, 317, 43, 1427, 37, 25693, 563, 17239, 911, 11497, 112247, 1259, 190639, 138569, 296713, 27733, 11777

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OFFSET

2,1

COMMENTS

All primes certified using openpfgw_v12 from primeform group

LINKS

Table of n, a(n) for n=2..27.

EXAMPLE

7*7-5*7-1=13 prime 7=M(2)=2^3-1 so k(2)=5;

31*31-7*31-1=743 prime 31=M(3)=2^5-1 so k(3)=7.

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; p = 1;

While[! PrimeQ[m2 - Prime[p]*m - 1], p++];

Prime[p], {n, 15}] (* Robert Price, Apr 17 2019 *)

CROSSREFS

Cf. A000668, A139424, A139425, A139426, A139427, A139429, A139430, A139421.

Sequence in context: A226660 A125294 A177735 * A303574 A063005 A329763

Adjacent sequences: A139425 A139426 A139427 * A139429 A139430 A139431

KEYWORD

hard,more,nonn

AUTHOR

Pierre CAMI, Apr 21 2008

STATUS

approved