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

1,1

Links

Table of n, a(n) for n=1..48.

Example

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

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;

Crossrefs

Sequence in context: A271043 A089056 A210981 * A255769 A175625 A082496

Adjacent sequences: A372300 A372301 A372302 * A372304 A372305 A372306

Keyword

nonn

Author

Stephen Bartell, May 22 2024

Status

approved