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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

%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

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Last modified April 19 08:45 EDT 2024. Contains 371782 sequences. (Running on oeis4.)