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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A108393 a(n)=number of primes of the form p^2+k^2 with 2<=k<=floor(sqrt(2*p+1)) (less than (p+1)^2), for every p(n).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 0, 1, 2, 1, 3, 2, 2, 0, 3, 1, 3, 2, 1, 3, 2, 5, 2, 2, 5, 2, 2, 3, 3, 1, 3, 2, 4, 3, 1, 1, 2, 1, 3, 4, 2, 2, 4, 1, 3, 2, 4, 3
Offset: 1

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Author

Robin Garcia, Jul 02 2005

Keywords

Comments

Conjecture: 23,83,113 and 811 are the only primes with a 0 value in the sequence. There is always a prime of the form p^2+k^2 (1 mod 4) between p^2 and (p+1)^2 for every prime not 23,83,113 or 811.

Examples

			a(5)=1 because p(5)=11 and very is only one value of k<=floor(sqrt(2*11+1))=4 for which p(5)^2+k^2 is prime: 11^2+4^2=137
a(27)=3 because p(27)=103 and 103^2+2^2=10613,103^2+10^2=10709,103^2+12^2=10753 are primes.

Crossrefs

Cf. A108714.
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