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

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

Author

Reinhard Zumkeller, Sep 07 2004

Keywords

• nonn

Comments

Convention: a prime triple is <= n iff its smallest member is <= n;

a(n) <= A098428(n).

Examples

			a(15) = #{(5,7,11),(7,11,13),(11,13,17),(13,17,19)} = 4.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Prime Triplet

Crossrefs

Cf. A007529, A098414, A098415, A071538.

Cf. A010051, A000040.

Programs

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

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 *)