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A098428 Number of sexy prime pairs (p, p+6) with p <= n. 6
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; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

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, Aug 05 2009]

LINKS

Daniel Forgues, Table of n, a(n) for n=1..99994

Eric Weisstein's World of Mathematics, Sexy Primes

EXAMPLE

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 ...

MATHEMATICA

Accumulate[Table[If[PrimeQ[n]&&PrimeQ[n+6], 1, 0], {n, 100}]] (* Harvey P. Dale, Feb 08 2015 *)

CROSSREFS

Cf. A023201, A046117, A098424, A071538, A098429.

Sequence in context: A209082 A257684 A098424 * A023193 A096605 A189671

Adjacent sequences:  A098425 A098426 A098427 * A098429 A098430 A098431

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Sep 07 2004

EXTENSIONS

Commented and edited by Daniel Forgues, Aug 01 2009

STATUS

approved

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Last modified April 23 22:17 EDT 2019. Contains 322388 sequences. (Running on oeis4.)