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

%I A098424 #11 Feb 16 2025 08:32:54
%S A098424 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,
%T A098424 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,
%U A098424 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
%N A098424 Number of prime triples (p,q,r) <= n with p<q<r=p+6.
%C A098424 Convention: a prime triple is <= n iff its smallest member is <= n;
%C A098424 a(n) <= A098428(n).
%H A098424 Harvey P. Dale, <a href="/A098424/b098424.txt">Table of n, a(n) for n = 1..1000</a>
%H A098424 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeTriplet.html">Prime Triplet</a>
%e A098424 a(15) = #{(5,7,11),(7,11,13),(11,13,17),(13,17,19)} = 4.
%t A098424 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 *)
%o A098424 (Haskell)
%o A098424 a098424 n = length [(p,q,r) | p <- takeWhile (<= n) a000040_list,
%o A098424             let r = p + 6, a010051 r == 1, q <- [p+1..r-1], a010051 q == 1]
%o A098424 -- _Reinhard Zumkeller_, Nov 15 2011
%Y A098424 Cf. A007529, A098414, A098415, A071538.
%Y A098424 Cf. A010051, A000040.
%K A098424 nonn
%O A098424 1,7
%A A098424 _Reinhard Zumkeller_, Sep 07 2004