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%I #15 Sep 08 2022 08:45:48
%S 1,2,2,2,4,3,4,2,4,4,3,4,4,2,4,4,4,4,4,4,5,4,4,6,3,5,4,5,3,4,5,6,6,6,
%T 6,8,2,4,4,3,2,6,8,4,5,4,5,6,6,5,4,5,4,5,7,8,5,7,6,8,8,8,3,3,2,4,6,7,
%U 6,4,4,6,8,3,5,3,5,6,7,7,7,7,4,4,6,7,6
%N Number of ones in the binary representation of the average of twin prime pairs.
%H Amiram Eldar, <a href="/A166008/b166008.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A000120(A014574(n)). - _Michel Marcus_, Dec 19 2019
%e Third twin prime pair = (11,13) with average 12 = 1100_2, with 2 ones, so a(3)=2.
%t seq={1}; Do[If[And @@ PrimeQ[6n + {-1, 1}], AppendTo[seq, DigitCount[6n, 2, 1]]], {n, 1, 600}]; seq (* _Amiram Eldar_, Dec 19 2019 *)
%t DigitCount[#,2,1]&/@(Mean/@Select[Partition[Prime[Range[1000]],2,1],#[[2]]- #[[1]] == 2&]) (* _Harvey P. Dale_, Dec 12 2021 *)
%o (Magma) [&+Intseq(p+1,2):p in PrimesUpTo(3000)|IsPrime(p+2)]; // _Marius A. Burtea_, Dec 19 2019
%Y Cf. A000120, A014574, A014499.
%K base,nonn
%O 1,2
%A Steven Lubars (lubars(AT)gmail.com), Oct 03 2009
%E More terms from _Amiram Eldar_, Dec 19 2019