A166008 Number of ones in the binary representation of the average of twin prime pairs.

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, 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, 6, 4, 4, 6, 8, 3, 5, 3, 5, 6, 7, 7, 7, 7, 4, 4, 6, 7, 6

Offset: 1

Author

Steven Lubars (lubars(AT)gmail.com), Oct 03 2009

Keywords

• base
• nonn

Examples

			Third twin prime pair = (11,13) with average 12 = 1100_2, with 2 ones, so a(3)=2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000120, A014574, A014499.

Programs

Magma

[&+Intseq(p+1,2):p in PrimesUpTo(3000)|IsPrime(p+2)]; // Marius A. Burtea, Dec 19 2019

Mathematica

seq={1}; Do[If[And @@ PrimeQ[6n + {-1, 1}], AppendTo[seq, DigitCount[6n, 2, 1]]], {n, 1, 600}]; seq (* Amiram Eldar, Dec 19 2019 *)
DigitCount[#,2,1]&/@(Mean/@Select[Partition[Prime[Range[1000]],2,1],#[[2]]- #[[1]] == 2&]) (* Harvey P. Dale, Dec 12 2021 *)

Formula

a(n) = A000120(A014574(n)). - Michel Marcus, Dec 19 2019

Extensions

More terms from Amiram Eldar, Dec 19 2019