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Search: id:A108393
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| A108393 |
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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). |
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+0
1
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| 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; listen)
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OFFSET
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1,10
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COMMENT
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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.
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EXAMPLE
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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.
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CROSSREFS
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Cf. A108714.
Sequence in context: A139755 A104637 A058745 this_sequence A062245 A062246 A037811
Adjacent sequences: A108390 A108391 A108392 this_sequence A108394 A108395 A108396
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KEYWORD
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nonn
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AUTHOR
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Robin Garcia (verob99(AT)teleline.es), Jul 02 2005
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