A098424 Number of prime triples (p,q,r) <= n with p<q<r=p+6.

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Cf. A007529, A098414, A098415, A071538.

Cf. A010051, A000040.

Sequence in context: A355880 A209082 A257684 * A098428 A023193 A096605

Adjacent sequences: A098421 A098422 A098423 * A098425 A098426 A098427

Keyword

nonn

Author

Reinhard Zumkeller, Sep 07 2004

Status

approved