A205649 Hamming distance between twin primes.

2, 1, 2, 1, 1, 1, 2, 3, 1, 2, 1, 1, 2, 6, 1, 2, 4, 1, 1, 3, 2, 2, 4, 1, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 7, 1, 1, 1, 1, 3, 2, 2, 1, 4, 3, 2, 2, 1, 1, 2, 4, 1, 2, 1, 1, 2, 1, 3, 6, 1, 1, 1, 2, 1, 2, 1, 1, 5, 1, 7, 3, 1, 1, 1, 1, 3, 4, 5, 2, 1, 2

Offset: 1

Author

Vladimir Shevelev, Jan 30 2012

Keywords

• nonn
• base

Comments

Twin primes for which a(n)=1 are in A122565.

Conjecture: The sequence is unbounded.

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A205510, A001097, A001359, A006512, A205302, A205511, A205533.

Programs

Mathematica

nn = 1000; ps = Prime[Range[nn]]; t = {}; Do[If[ps[[n]] + 2 == ps[[n + 1]], AppendTo[t, ps[[n]]]], {n, nn - 1}]; Table[b2 = IntegerDigits[t[[k]] + 2, 2];  b1 = IntegerDigits[t[[k]], 2, Length[b2]]; Total[Abs[b1 - b2]], {k, Length[t]}] (* T. D. Noe, Jan 30 2012 *)

Formula

A001359(n) == -1 (mod 2^a(n)).