login
Primes p such that there exists prime q < p for which p*q^2 + 1 is divisible by q^2 + p and 1 + p.
0

%I #25 Jun 10 2024 18:45:09

%S 7,11,23,31,41,47,59,71,79,131,137,151,167,239,311,359,443,461,701,

%T 839,911,1021,1039,1367,1721,1847,2207,2351,2551,2861,3191,3719,4019,

%U 4691,4759,5039,5167,5279,6971,7481,7853,7919,9311,9619,9689,10607,10739,11447

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

%p P:= select(isprime,[2,seq(i,i=3..100000,2)]):

%p nP:= nops(P);

%p R:= NULL:

%p for i from 2 to nP do

%p p:= P[i];

%p for j from 1 to i-1 do

%p q:= P[j];

%p if p*q^2 + 1 mod ilcm(p+1, q^2+p) = 0 then

%p R:= R,p;

%p break

%p fi

%p od od:

%p R;

%K nonn

%O 1,1

%A _Stephen Bartell_, May 22 2024