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%I #6 Jan 13 2023 09:18:29
%S 0,1,2,4,6,9,12,15,19,23,27,32,37,42,48,54,60,66,73,80,87,94,101,109,
%T 117,125,133,142,151,160,169
%N a(n) = n*(n+1)/2 - A156022(n).
%C 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.
%H 2008/9 British Mathematical Olympiad Round 2, <a href="http://www.bmoc.maths.org/home/bmo2-2009.pdf">Problem 4</a>, Jan 29 2009.
%F 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.
%Y Cf. A078822, A112509, A112510, A112511, A122953, A156022, A156023, A156025.
%Y Equals A156023(n)+1 for n >= 2.
%K nonn,base,more
%O 1,3
%A _Joseph Myers_, Feb 01 2009
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