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A257362
Odd primes modulo which -163 is a square.
4
41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 163, 167, 173, 179, 197, 199, 223, 227, 251, 263, 281, 307, 313, 347, 359, 367, 373, 379, 383, 397, 409, 419, 421, 439, 457, 461, 487, 499, 503, 523, 547, 563, 577, 593, 607, 641, 647, 653, 661, 673, 677, 691
OFFSET
1,1
COMMENTS
Contains A005846. The first members that are not in A005846 are 163 and 167.
Primes that divide some member of A202018.
Primes congruent to x^2 mod 163 for some x, 0 <= x <= 162.
Primes of the form x^2 + xy + 41y^2. Also, primes of the form x^2 - xy + 41y^2 with x and y nonnegative. - Jianing Song, Feb 19 2021
LINKS
FORMULA
a(n) ~ 2n log n. - Charles R Greathouse IV, Nov 28 2016
MAPLE
select(p -> isprime(p) and (p=163 or numtheory:-legendre(-163, p)=1), [seq(2*i+1, i=1..1000)]);
# Another Maple program is given in A296920. - N. J. A. Sloane, Dec 25 2017
MATHEMATICA
Reap[For[p=3, p<1000, p = NextPrime[p], If[p==163 || KroneckerSymbol[-163, p] == 1, Print[p]; Sow[p]]]][[2, 1]] (* Jean-François Alcover, Apr 29 2019 *)
PROG
(PARI) is(n)=isprime(n) && issquare(Mod(-163, n)) \\ Charles R Greathouse IV, Nov 28 2016
CROSSREFS
Sequence in context: A118124 A054057 A282319 * A330673 A296921 A202018
KEYWORD
nonn,easy
AUTHOR
Robert Israel, Apr 20 2015
STATUS
approved