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 A219315 Smallest prime of the form LegendreP[2*n, k], k integer > 0. 5
 13, 10321, 1651609, 265729, 2418383311848550201, 143457011569, 4788279267715459491640247899801, 55836455668763269069656769, 21624792044006209908534390421, 996389426180855801077045825760311681, 97188318826075110353523764096667396436794217 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS LegendreP [2*n, x] is the 2*n th Legendre polynomial of the first kind evaluated at x. The corresponding values k are in A219313. REFERENCES 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. LINKS Table of n, a(n) for n=1..11. Eric Weisstein's World of Mathematics, Legendre Polynomial EXAMPLE a(1) = 13 because LegendreP [2*1, x] = (3x^2 - 1)/2 and LegendreP[2,3] = 13 is prime, where 3 = A219313(1). MATHEMATICA Table[k=0; While[!PrimeQ[LegendreP [2*n, k]], k++]; LegendreP [2*n, k], {n, 20}] PROG (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 CROSSREFS Cf. A219313. Sequence in context: A173506 A173840 A260457 * A068731 A189309 A203707 Adjacent sequences: A219312 A219313 A219314 * A219316 A219317 A219318 KEYWORD nonn AUTHOR Michel Lagneau, Nov 17 2012 STATUS approved

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Last modified September 29 12:11 EDT 2023. Contains 365771 sequences. (Running on oeis4.)