login
A219313
Smallest number k such that LegendreP[2*n, k] is prime.
1
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
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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Nov 17 2012
STATUS
approved