%I #11 Jan 01 2023 02:58:55
%S 7,11,23,109,211,1021,42967,297779,125211211,11673806759
%N Primes prime(k) such that prime(k)^2 + prime(k+1)^2  1 is the square of a prime.
%C Suggested in an email from _J. M. Bergot_.
%C There are no more terms < 10^100 unless the prime gap g = prime(k+1)  prime(k) exceeds 10000. For all known terms, g <= 14. There are no more terms < 10^1000 with g <= 14.  _Jon E. Schoenfield_, Dec 31 2022
%e a(3) = 23 is a term because 23 is prime, the next prime is 29, and 23^2 + 29^2  1 = 37^2 where 37 is prime.
%p R:= NULL: q:= 2:
%p while q < 2*10^8 do
%p p:= q; q:= nextprime(q);
%p r:= p^2 + q^2  1;
%p if issqr(r) and isprime(sqrt(r)) then R:= R, p fi
%p od:
%p R;
%Y Subset of A160054.
%K nonn,more,less
%O 1,1
%A _Robert Israel_, Dec 30 2022
