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A156024
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a(n) = n*(n+1)/2 - A156022(n).
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6
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0, 1, 2, 4, 6, 9, 12, 15, 19, 23, 27, 32, 37, 42, 48, 54, 60, 66, 73, 80, 87, 94, 101, 109, 117, 125, 133, 142, 151, 160, 169
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OFFSET
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1,3
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COMMENTS
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n(n+1)/2 is the total number of nonempty substrings of an n-bit binary number; A156022 is the maximum number of substrings representing distinct positive integers.
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LINKS
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2008/9 British Mathematical Olympiad Round 2, Problem 4, Jan 29 2009.
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FORMULA
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c_1 + o(1) <= a(n)/n^1.5 <= c_2 + o(1) for some positive constants c_1 and c_2; it seems likely a(n)/n^1.5 tends to some positive constant limit.
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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STATUS
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approved
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