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 A219315 #7 Feb 16 2025 08:33:18
%S A219315 13,10321,1651609,265729,2418383311848550201,143457011569,
%T A219315 4788279267715459491640247899801,55836455668763269069656769,
%U A219315 21624792044006209908534390421,996389426180855801077045825760311681,97188318826075110353523764096667396436794217
%N A219315 Smallest prime of the form LegendreP[2*n, k], k integer > 0.
%C A219315 LegendreP [2*n, x] is the 2*n th Legendre polynomial of the first kind evaluated at x.
%C A219315 The corresponding values k are in A219313.
%D A219315 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 798.
%H A219315 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LegendrePolynomial.html">Legendre Polynomial</a>
%e A219315 a(1) = 13 because LegendreP [2*1, x] = (3x^2 - 1)/2 and LegendreP[2,3] = 13 is prime, where 3 = A219313(1).
%t A219315 Table[k=0;While[!PrimeQ[LegendreP [2*n,k]],k++]; LegendreP [2*n,k],{n,20}]
%o A219315 (PARI) a(n)=my(P=pollegendre(2*n),k,t); while(denominator(t=subst(P,'x,k++))>1 || !ispseudoprime(t),); t \\ _Charles R Greathouse IV_, Mar 18 2017
%Y A219315 Cf. A219313.
%K A219315 nonn
%O A219315 1,1
%A A219315 _Michel Lagneau_, Nov 17 2012