A103863 Hamming distance between n and A102370(n) (in binary).

0, 1, 1, 2, 0, 2, 2, 3, 0, 1, 1, 2, 1, 3, 3, 4, 0, 1, 1, 2, 0, 2, 2, 3, 0, 1, 1, 3, 2, 4, 4, 5, 0, 1, 1, 2, 0, 2, 2, 3, 0, 1, 1, 2, 1, 3, 3, 4, 0, 1, 1, 2, 0, 2, 2, 3, 0, 1, 2, 4, 3, 5, 5, 6, 0, 1, 1, 2, 0, 2, 2, 3, 0, 1, 1, 2, 1, 3, 3, 4, 0, 1, 1, 2, 0, 2, 2, 3, 0, 1, 1, 3, 2, 4, 4, 5, 0, 1, 1, 2, 0, 2, 2, 3, 0

Offset

0,4

Comments

The Hamming distance between two strings of the same length is the number of places where they differ. - Robert G. Wilson v, Apr 12 2005

References

F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 8.

Links

Table of n, a(n) for n=0..104.

David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].

David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.

Saleem Bhatti, Channel coding; Hamming distance.

Alexander Bogomolny, Distance Between Strings.

National Institute of Standards and Technology, Hamming distance.

Formula

a(A104235(n)) = 0.

Mathematica

f[n_] := Block[{k = 1, s = 0, l = Max[2, Floor[ Log[2, n + 1] + 2]]}, While[ k < l, If[ Mod[n + k, 2^k] == 0, s = s + 2^k]; k++ ]; s]; hammingdistance[n_] := Count[ IntegerDigits[ BitXor[n, f[n] + n], 2], 1]; Table[ hammingdistance[n], {n, 0, 104}] (* Robert G. Wilson v, Apr 12 2005 *)

Crossrefs

Cf. A102370, A103542, A104235.

Sequence in context: A101276 A339434 A348325 * A166395 A378990 A061199

Adjacent sequences: A103860 A103861 A103862 * A103864 A103865 A103866

Keyword

nonn,easy,base

Author

Philippe Deléham, Mar 31 2005

Extensions

More terms from Robert G. Wilson v, Apr 12 2005

Status

approved