A038880 Primes p such that 10 is not a square mod p.

7, 11, 17, 19, 23, 29, 47, 59, 61, 73, 97, 101, 103, 109, 113, 127, 131, 137, 139, 149, 167, 179, 181, 193, 211, 223, 229, 233, 251, 257, 263, 269, 313, 331, 337, 349, 353, 367, 379, 383, 389, 419, 421, 433, 457, 461, 463, 487, 491, 499, 503, 509, 541, 571

Offset

1,1

Comments

Inert rational primes in the field Q(sqrt(10)). - N. J. A. Sloane, Dec 26 2017

Also primes p such that p divides 5^(p-1)/2 + 2^(p-1)/2. - Cino Hilliard, Sep 06 2004

All primes p such that (p^2 - 1)/24 mod 10 = {2,5}. - Richard R. Forberg, Aug 31 2013

Primes that are 7, 11, 17, 19, 21, 23, 29, or 33 mod 40. - Charles R Greathouse IV, Mar 18 2018

Primes p such that p-1 divided by the number of the digits of the period of 1/p results in an odd number. - Davide Rotondo, Apr 28 2024

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index to sequences related to decomposition of primes in quadratic fields

Formula

a(n) ~ 2n log n. - Charles R Greathouse IV, Mar 18 2018

Mathematica

Select[ Prime@Range[2, 105], JacobiSymbol[10, # ] == -1 &] (* Robert G. Wilson v, Dec 15 2005 *)

Prog

(PARI) list(lim)=my(v=List()); forprime(p=7, lim, if(kronecker(10, p)<0, listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Mar 18 2018
(Python)
from sympy import isprime, jacobi_symbol
def ok(n): return n%2 == 1 and isprime(n) and jacobi_symbol(10, n) == -1
print([k for k in range(575) if ok(k)]) # Michael S. Branicky, May 24 2022

Crossrefs

Cf. A007348.

Sequence in context: A269256 A106070 A346991 * A019365 A191055 A078497

Adjacent sequences: A038877 A038878 A038879 * A038881 A038882 A038883

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Robert G. Wilson v, Dec 15 2005

Status

approved