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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

%I

%S 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,

%T 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

%N 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).

%C 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.

%e 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

%e 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.

%Y Cf. A108714.

%K nonn

%O 1,10

%A _Robin Garcia_, Jul 02 2005

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Last modified January 26 16:14 EST 2023. Contains 359833 sequences. (Running on oeis4.)