cp's OEIS Frontend

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.

%I A372303 #25 Jun 10 2024 18:45:09
%S A372303 7,11,23,31,41,47,59,71,79,131,137,151,167,239,311,359,443,461,701,
%T A372303 839,911,1021,1039,1367,1721,1847,2207,2351,2551,2861,3191,3719,4019,
%U A372303 4691,4759,5039,5167,5279,6971,7481,7853,7919,9311,9619,9689,10607,10739,11447
%N 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.
%e A372303 For n=4, a(4)=31 and q=17 satisfy the desired divisibilities.
%p A372303 P:= select(isprime,[2,seq(i,i=3..100000,2)]):
%p A372303 nP:= nops(P);
%p A372303 R:= NULL:
%p A372303 for i from 2 to nP do
%p A372303   p:= P[i];
%p A372303   for j from 1 to i-1 do
%p A372303     q:= P[j];
%p A372303     if p*q^2 + 1 mod ilcm(p+1, q^2+p) = 0 then
%p A372303       R:= R,p;
%p A372303       break
%p A372303     fi
%p A372303 od od:
%p A372303 R;
%K A372303 nonn
%O A372303 1,1
%A A372303 _Stephen Bartell_, May 22 2024