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 A156023 #14 Jul 25 2025 02:19:01 %S A156023 0,0,1,3,5,8,11,14,18,22,26,31,36,41,47,53,59,65,72,79,86,93,100,108, %T A156023 116,124,132,141,150,159,168,177,186,196,206,216,226,237,248,259,270, %U A156023 281,292,303,315,327,339,351,363,376,389,401,414,427,440,453,467,481 %N A156023 a(n) = n*(n+1)/2 - A112509(n). %C A156023 n(n+1)/2 is the total number of nonempty substrings of an n-bit binary number; A112509 is the maximum number of substrings representing distinct integers. %H A156023 Martin Fuller, <a href="/A156023/b156023.txt">Table of n, a(n) for n = 1..80</a> %H A156023 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 A156023 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 A156023 Cf. A000217, A078822, A112509, A112510, A112511, A122953, A156022, A156024, A156025. Equals A156024(n)-1 for n >= 2. %K A156023 nonn,base %O A156023 1,4 %A A156023 _Joseph Myers_, Feb 01 2009 %E A156023 a(32) onwards from _Martin Fuller_, Jul 24 2025