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A098424
Number of prime triples (p,q,r) <= n with p<q<r=p+6.
4
0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 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, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 11
OFFSET
1,7
COMMENTS
Convention: a prime triple is <= n iff its smallest member is <= n;
a(n) <= A098428(n).
LINKS
Eric Weisstein's World of Mathematics, Prime Triplet
EXAMPLE
a(15) = #{(5,7,11),(7,11,13),(11,13,17),(13,17,19)} = 4.
MATHEMATICA
With[{pts=Select[Partition[Prime[Range[1200]], 3, 1], Last[#]-First[#] == 6&]}, Table[Count[pts, _?(First[#]<=n&)], {n, 110}]] (* Harvey P. Dale, Nov 09 2011 *)
PROG
(Haskell)
a098424 n = length [(p, q, r) | p <- takeWhile (<= n) a000040_list,
let r = p + 6, a010051 r == 1, q <- [p+1..r-1], a010051 q == 1]
-- Reinhard Zumkeller, Nov 15 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Sep 07 2004
STATUS
approved