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

Author

Michel Lagneau, Nov 17 2012

Keywords

• nonn

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.

Examples

			a(1) = 13 because LegendreP [2*1, x] = (3x^2 - 1)/2  and LegendreP[2,3] = 13 is prime, where 3 = A219313(1).
		

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

• Eric Weisstein's World of Mathematics, Legendre Polynomial

Crossrefs

Cf. A219313.

Programs

Mathematica

Table[k=0;While[!PrimeQ[LegendreP [2*n,k]],k++]; LegendreP [2*n,k],{n,20}]

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