A219313 Smallest number k such that LegendreP[2*n, k] is prime.

3, 7, 7, 3, 41, 5, 89, 23, 21, 35, 55, 5, 181, 511, 241, 83, 709, 401, 3653, 901, 137, 497, 1411, 121, 281, 209, 201, 191, 1667, 89, 39, 181, 233, 2783, 85, 911, 1717, 919, 97, 1163, 1319, 971, 361, 2371, 1573, 121, 817, 733, 1657, 1895, 509, 431, 2399, 1483

Offset

1,1

Comments

LegendreP [2*n, x] is the 2*n th Legendre polynomial of the first kind evaluated at x.

The corresponding primes are in A219315.

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..54.

Eric Weisstein's World of Mathematics, Legendre Polynomial

Example

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

Mathematica

Table[k = 0; While[!PrimeQ[LegendreP [2*n, k]], k++]; k, {n, 70}]

Prog

(PARI) a(n)=my(P=pollegendre(2*n), k, t); while(denominator(t=subst(P, 'x, k++))>1 || !ispseudoprime(t), ); k \\ Charles R Greathouse IV, Mar 18 2017

Crossrefs

Cf. A219315.

Sequence in context: A021269 A199277 A346588 * A354966 A021730 A153844

Adjacent sequences: A219310 A219311 A219312 * A219314 A219315 A219316

Keyword

nonn

Author

Michel Lagneau, Nov 17 2012

Status

approved