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A098429
Number of cousin prime pairs (p, p+4) with p <= n.
4
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
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Sep 07 2004
EXTENSIONS
Edited by Daniel Forgues, Aug 01 2009
STATUS
approved