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A126387
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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).
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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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).
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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.
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CROSSREFS
| Cf. A036989.
Sequence in context: A144790 A090996 A089309 * A038374 A161161 A136277
Adjacent sequences: A126384 A126385 A126386 * A126388 A126389 A126390
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KEYWORD
| easy,nonn
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AUTHOR
| Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Dec 26 2006
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