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

1,1

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

Formula

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

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 *)

Crossrefs

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

Sequence in context: A029433 A337144 A088203 * A176510 A362951 A342464

Adjacent sequences: A205646 A205647 A205648 * A205650 A205651 A205652

Keyword

nonn,base

Author

Vladimir Shevelev, Jan 30 2012

Status

approved