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 A359414 Primes prime(k) such that prime(k)^2 + prime(k+1)^2 - 1 is the square of a prime. 0
 7, 11, 23, 109, 211, 1021, 42967, 297779, 125211211, 11673806759 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 LINKS Table of n, a(n) for n=1..10. EXAMPLE 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. 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; CROSSREFS Subset of A160054. Sequence in context: A181841 A076855 A160054 * A247590 A027830 A134043 Adjacent sequences: A359411 A359412 A359413 * A359415 A359416 A359417 KEYWORD nonn,more,less AUTHOR Robert Israel, Dec 30 2022 STATUS approved

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Last modified February 25 02:17 EST 2024. Contains 370308 sequences. (Running on oeis4.)