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A359414
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Primes prime(k) such that prime(k)^2 + prime(k+1)^2 - 1 is the square of a prime.
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0
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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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.
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MAPLE
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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;
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CROSSREFS
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KEYWORD
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nonn,more,less
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AUTHOR
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STATUS
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approved
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