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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). 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 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. LINKS EXAMPLE 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. Sequence in context: A325444 A058745 A275333 * A327342 A297828 A062245 Adjacent sequences: A108390 A108391 A108392 * A108394 A108395 A108396 KEYWORD nonn AUTHOR Robin Garcia, Jul 02 2005 STATUS approved

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Last modified December 3 03:47 EST 2022. Contains 358511 sequences. (Running on oeis4.)