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%I #8 Apr 17 2019 19:06:50
%S 3,3,5,17,17,5,83,503,71,101,947,59,569,1787,353,17093,2801,3359,
%T 25097,9323,491837,97367,209567,21221,273857,462947,216719
%N Smallest prime p such that M(n)^2+p*M(n)+1 is prime with M(n)= Mersenne primes =A000668(n).
%C All primes certified using openpfgw_v12 from primeform group
%e 3*3+3*3+1=19 prime 3=M(1)=2^2-1 so p(1)=3;
%e 7*7+3*7+1=71 prime 7=M(2)=2^3-1 so p(2)=3;
%e 31*31+5*31+1=1117 prime 31=M(3)=2^5-1 so p(3)=5.
%t 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};
%t Table[m = 2^A000043[[n]] - 1; m2 = m^2; p = 1;
%t While[! PrimeQ[m2 + Prime[p]*m + 1], p++];
%t Prime[p], {n, 15}] (* _Robert Price_, Apr 17 2019 *)
%Y Cf. A000668, A139424, A139425, A139426, A139427, A139428, A139429, A139430.
%K hard,more,nonn
%O 1,1
%A _Pierre CAMI_, Apr 21 2008
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