This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A156024 #12 Jul 24 2025 20:59:42 %S A156024 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 A156024 117,125,133,142,151,160,169,178,187,197,207,217,227,238,249,260,271, %U A156024 282,293,304,316,328,340,352,364,377,390,402,415,428,441,454,468,482 %N A156024 a(n) = n*(n+1)/2 - A156022(n). %C A156024 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 A156024 Martin Fuller, <a href="/A156024/b156024.txt">Table of n, a(n) for n = 1..80</a> %H A156024 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 A156024 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 A156024 Cf. A000217, A078822, A112509, A112510, A112511, A122953, A156022, A156023, A156025. %Y A156024 Equals A156023(n)+1 for n >= 2. %K A156024 nonn,base %O A156024 1,3 %A A156024 _Joseph Myers_, Feb 01 2009 %E A156024 a(32) onwards from _Martin Fuller_, Jul 24 2025