A219315 Smallest prime of the form LegendreP[2*n, k], k integer > 0.

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

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