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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
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
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.)