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

Author

Benoit Cloitre, May 10 2002

Keywords

• easy
• nonn

Links

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

Programs

Mathematica

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

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

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