A071702 - OEIS

%I #10 Nov 12 2021 19:36:38

%S 0,0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,

%T 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,

%U 3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4

%N Number of twin prime pairs <= n of form (4*k+3,4*(k+1)+1), k>=0.

%C As for A071538 the convention is followed that a twin prime pair is <= n if its smaller member is <= n.

%C If {a,b} is a twin prime pair (a<b), and Mod[a,4]==3, there is no need to test b because it must be 1 Mod 4. - _Harvey P. Dale_, Nov 12 2021

%H Harvey P. Dale, <a href="/A071702/b071702.txt">Table of n, a(n) for n = 1..1000</a>

%e a(60)=3, since (59,61) is included along with (3,5) and (11,13).

%t Accumulate[Table[If[AllTrue[{n,n+2},PrimeQ]&&Mod[n,4]==3,1,0],{n,100}]] (* _Harvey P. Dale_, Nov 12 2021 *)

%Y a(n) = A071538(n) - A071701(n), cf. A071698, A071699.

%K nonn

%O 1,11

%A _Reinhard Zumkeller_, Jun 04 2002