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 A139429 #11 Apr 18 2019 06:33:38
%S A139429 3,19,3,3,73,7,271,1021,241,3,487,151,2971,35839,5737,1723,81943,
%T A139429 115741,307,151549,231823,443431,195163,9973,114913,362599
%N A139429 Smallest prime p such that M(n)^2 - p*M(n) + 1 is prime with M(n) = A000668(n).
%C A139429 All primes certified using openpfgw_v12 from primeform group.
%e A139429 7*7-3*7+1=29 prime 7=M(2)=2^3-1 so k(2)=3;
%e A139429 31*31-19*31+1=373 prime 31=M(3)=2^5-1 so k(3)=19.
%t A139429 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 A139429 Table[m = 2^A000043[[n]] - 1; m2 = m^2; p = 1;
%t A139429 While[! PrimeQ[m2 - Prime[p]*m + 1], p++];
%t A139429 Prime[p], {n, 15}] (* _Robert Price_, Apr 17 2019 *)
%Y A139429 Cf. A000668, A139424, A139425, A139426, A139427, A139428, A139430, A139421.
%K A139429 hard,more,nonn
%O A139429 2,1
%A A139429 _Pierre CAMI_, Apr 21 2008