A359414 Primes prime(k) such that prime(k)^2 + prime(k+1)^2 - 1 is the square of a prime.

7, 11, 23, 109, 211, 1021, 42967, 297779, 125211211, 11673806759

Offset: 1

Author

Robert Israel, Dec 30 2022

Keywords

• nonn
• more
• less

Comments

Suggested in an email from J. M. Bergot.

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

Examples

			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.
		

Crossrefs

Subset of A160054.

Programs

Maple

R:= NULL: q:= 2:
while q < 2*10^8 do
  p:= q; q:= nextprime(q);
r:= p^2 + q^2 - 1;
  if issqr(r) and isprime(sqrt(r)) then R:= R, p fi
od:
R;