A372303 Primes p such that there exists prime q < p for which p*q^2 + 1 is divisible by q^2 + p and 1 + p.

7, 11, 23, 31, 41, 47, 59, 71, 79, 131, 137, 151, 167, 239, 311, 359, 443, 461, 701, 839, 911, 1021, 1039, 1367, 1721, 1847, 2207, 2351, 2551, 2861, 3191, 3719, 4019, 4691, 4759, 5039, 5167, 5279, 6971, 7481, 7853, 7919, 9311, 9619, 9689, 10607, 10739, 11447

Offset: 1

Author

Stephen Bartell, May 22 2024

Keywords

• nonn

Examples

			For n=4, a(4)=31 and q=17 satisfy the desired divisibilities.
		

Programs

Maple

P:= select(isprime,[2,seq(i,i=3..100000,2)]):
nP:= nops(P);
R:= NULL:
for i from 2 to nP do
  p:= P[i];
  for j from 1 to i-1 do
    q:= P[j];
    if p*q^2 + 1 mod ilcm(p+1, q^2+p) = 0 then
      R:= R,p;
      break
    fi
od od:
R;