This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A139427 #8 Apr 17 2019 19:06:17
%S A139427 1,3,5,17,17,5,83,63,71,101,543,59,569,1029,353,1851,2801,2619,525,
%T A139427 2907,8955,437,30159,5409,8355
%N A139427 Smallest number k such that M(n)^2+k*M(n)+1 is prime with M(n)= Mersenne primes =A000668(n).
%C A139427 All primes certified using openpfgw_v12 from primeform group
%e A139427 3*3+1*3+1=13 prime 3=M(1)=2^2-1 so k(1)=1;
%e A139427 7*7+3*7+1=71 prime 7=M(2)=2^3-1 so k(2)=3;
%e A139427 31*31+5*31+1=1117 prime 31=M(3)=2^5-1 so k(3)=5.
%t A139427 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 A139427 Table[m = 2^A000043[[n]] - 1; m2 = m^2; k = 1;
%t A139427 While[! PrimeQ[m2 + k*m + 1], k++]; k, {n, 15}] (* _Robert Price_, Apr 17 2019 *)
%Y A139427 Cf. A000668, A139424, A139425, A139426, A139428, A139429, A139430, A139421.
%K A139427 hard,more,nonn
%O A139427 1,2
%A A139427 _Pierre CAMI_, Apr 21 2008