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A219315

Smallest prime of the form LegendreP[2*n, k], k integer > 0.

13, 10321, 1651609, 265729, 2418383311848550201, 143457011569, 4788279267715459491640247899801, 55836455668763269069656769, 21624792044006209908534390421, 996389426180855801077045825760311681, 97188318826075110353523764096667396436794217

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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