A098429 Number of cousin prime pairs (p, p+4) with p <= n.

0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10

Offset

1,7

Comments

Convention: a prime pair is <= n iff its smallest member is <= n.

Except for (3, 7), there is only 1 pair congruence class for cousin primes, i.e. (+1, -1) (mod 6). [Daniel Forgues, Aug 05 2009]

Links

Daniel Forgues, Table of n, a(n) for n=1..99996

Eric Weisstein's World of Mathematics, Cousin Primes

Example

First cousin prime pairs: (3,7),(7,11),(13,17),(19,23), ...
therefore the sequence starts: 0 0 1 1 1 1 2 2 2 2 2 2 3 ...

Mathematica

Accumulate[Table[If[PrimeQ[i]&&PrimeQ[i+4], 1, 0], {i, 1, 100}]] (* Seiichi Kirikami, May 28 2017 *)

Crossrefs

Cf. A023200, A046132, A098428, A071538.

Sequence in context: A264749 A240567 A067099 * A132090 A235043 A071538

Adjacent sequences: A098426 A098427 A098428 * A098430 A098431 A098432

Keyword

nonn

Author

Reinhard Zumkeller, Sep 07 2004

Extensions

Edited by Daniel Forgues, Aug 01 2009

Status

approved