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A205649
Hamming distance between twin primes.
15
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.
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 *)
KEYWORD
nonn,base
AUTHOR
Vladimir Shevelev, Jan 30 2012
STATUS
approved