A126387 Read binary expansion of n from the left; keep track of the excess of 1's over 0's that have been seen so far; sequence gives maximum(excess of 1's over 0's).

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

Offset

0,4

Links

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

Formula

a(0) = 0, a(2^i) = 1, if n = 2^i + 2^j + m with j < i and 0 <= m < 2^j, then a(n) = max(a(2^j+m) + j + 2 - i, 1).

Example

59 in binary is 111011, excess from left to right is 1,2,3,2,3,4, maximum is 4, so a(59) = 4.

Crossrefs

Cf. A036989.

Sequence in context: A237453 A265754 A089309 * A038374 A284569 A272604

Adjacent sequences: A126384 A126385 A126386 * A126388 A126389 A126390

Keyword

easy,nonn

Author

Franklin T. Adams-Watters, Dec 26 2006

Status

approved