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A139431 Smallest prime p such that M(n)^2+p*M(n)+1 is prime with M(n)= Mersenne primes =A000668(n). 1
3, 3, 5, 17, 17, 5, 83, 503, 71, 101, 947, 59, 569, 1787, 353, 17093, 2801, 3359, 25097, 9323, 491837, 97367, 209567, 21221, 273857, 462947, 216719 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All primes certified using openpfgw_v12 from primeform group

LINKS

Table of n, a(n) for n=1..27.

EXAMPLE

3*3+3*3+1=19 prime 3=M(1)=2^2-1 so p(1)=3;

7*7+3*7+1=71 prime 7=M(2)=2^3-1 so p(2)=3;

31*31+5*31+1=1117 prime 31=M(3)=2^5-1 so p(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; 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, A139428, A139429, A139430.

Sequence in context: A051684 A209388 A195583 * A144423 A128636 A123633

Adjacent sequences:  A139428 A139429 A139430 * A139432 A139433 A139434

KEYWORD

hard,more,nonn

AUTHOR

Pierre CAMI, Apr 21 2008

STATUS

approved

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Last modified December 7 03:00 EST 2019. Contains 329836 sequences. (Running on oeis4.)