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A257362 Odd primes modulo which -163 is a square. 3
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 (list; graph; refs; listen; history; text; internal format)
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

Robert Israel, Table of n, a(n) for n = 1..10000

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-Fran├žois Alcover, Apr 29 2019 *)

PROG

(PARI) is(n)=isprime(n) && issquare(Mod(-163, n)) \\ Charles R Greathouse IV, Nov 28 2016

CROSSREFS

Cf. A005846, A202018.

Sequence in context: A118124 A054057 A282319 * A330673 A296921 A155884

Adjacent sequences:  A257359 A257360 A257361 * A257363 A257364 A257365

KEYWORD

nonn,easy

AUTHOR

Robert Israel, Apr 20 2015

STATUS

approved

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Last modified October 19 14:00 EDT 2021. Contains 348090 sequences. (Running on oeis4.)