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).

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

1,10

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

Table of n, a(n) for n=1..64.

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