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Search: id:A098428
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| A098428 |
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Number of sexy prime pairs (p, p+6) with p <= n. |
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+0
5
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| 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15
(list; graph; listen)
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OFFSET
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1,7
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COMMENT
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Convention: a prime pair is <= n iff its smallest member is <= n.
Since there are 2 congruence classes of sexy prime pairs, (-1, -1) (mod 6) and (+1, +1) (mod 6), the number of sexy prime pairs up to n is the sum of the number of sexy prime pairs for each class, expected to be asymptotically the same for both (with the expected Chebyshev bias against the quadratic residue class (+1, +1) (mod 6), which doesn't affect the asymptotic distribution among the 2 classes.) [From Daniel Forgues (squid(AT)zenearch.com), Aug 05 2009]
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LINKS
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Daniel Forgues, Table of n, a(n) for n=1..99994
Eric Weisstein's World of Mathematics, Sexy Primes
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EXAMPLE
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First sexy prime pairs: (5,11),(7,13),(11,17),(13,19), ...
therefore the sequence starts: 0 0 0 0 1 1 2 2 2 2 3 3 4 ...
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CROSSREFS
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Cf. A023201, A046117, A098424, A071538, A098429.
Sequence in context: A048273 A024542 A098424 this_sequence A023193 A096605 A109497
Adjacent sequences: A098425 A098426 A098427 this_sequence A098429 A098430 A098431
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 07 2004
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EXTENSIONS
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Commented and edited by Daniel Forgues (squid(AT)zensearch.com), Aug 01 2009
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