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

1,2

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000120, A014574, A014499.

Sequence in context: A083403 A114091 A209580 * A194291 A194323 A070867

Adjacent sequences: A166005 A166006 A166007 * A166009 A166010 A166011

Keyword

base,nonn

Author

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

Extensions

More terms from Amiram Eldar, Dec 19 2019

Status

approved