A070303 Primes p such that the equation p^2*x^2==0 (mod p^2+x^2) has no solution.

3, 7, 11, 13, 19, 23, 29, 31, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 199, 211, 223, 227, 229, 233, 239, 241, 251, 263, 269, 271, 277, 281, 283, 293, 307, 311

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

Primes not in A002496 (i.e., not of the form k^2+1).

a(n) ~ n log n. - Charles R Greathouse IV, Sep 30 2012

Mathematica

Select[Range[320], PrimeQ[#] && !IntegerQ @ Sqrt[# - 1] &] (* Amiram Eldar, Sep 11 2019 *)

Prog

(PARI) for(n=1, 350, if(0==sum(i=1, n^2, if((n^2*i^2)%(n^2+i^2), 1-isprime(n), 1)), print1(n, ", ")))
(PARI) is(n)=isprime(n) && !issquare(n-1) \\ Charles R Greathouse IV, Sep 30 2012
(PARI) print1(3); forstep(k=2, 9, 2, forprime(p=k^2+3, (k+2)^2, print1(", "p))) \\ Charles R Greathouse IV, Sep 30 2012

Crossrefs

Sequence in context: A310197 A360077 A090456 * A256863 A136087 A091250

Adjacent sequences: A070300 A070301 A070302 * A070304 A070305 A070306

Keyword

easy,nonn

Author

Benoit Cloitre, May 10 2002

Status

approved