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

Author

Philippe Deléham, Mar 31 2005

Keywords

• nonn
• easy
• base

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

• 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.

Crossrefs

Cf. A102370, A103542, A104235.

Programs

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 *)

Formula

a(A104235(n)) = 0.

Extensions

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