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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

Crossrefs

Cf. A007348.

Programs

Mathematica

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

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

Formula

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

Extensions

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