A156024 a(n) = n*(n+1)/2 - A156022(n).

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

Offset

1,3

Comments

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.

Links

Table of n, a(n) for n=1..31.

2008/9 British Mathematical Olympiad Round 2, Problem 4, Jan 29 2009.

Formula

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.

Crossrefs

Cf. A078822, A112509, A112510, A112511, A122953, A156022, A156023, A156025.

Equals A156023(n)+1 for n >= 2.

Sequence in context: A376343 A003066 A075349 * A234363 A194229 A194201

Adjacent sequences: A156021 A156022 A156023 * A156025 A156026 A156027

Keyword

nonn,base,more

Author

Joseph Myers, Feb 01 2009

Status

approved