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 A382288 #10 May 06 2025 00:34:46 %S A382288 0,1,1,1,1,1,2,1,1,1,1,1,2,2,2,1,1,1,1,1,2,1,1,1,2,2,2,2,2,2,2,1,1,1, %T A382288 1,1,1,1,1,1,2,2,1,1,2,1,1,1,2,2,2,2,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1, %U A382288 1,1,1,1,2,1,1,1,1,1,1,1,2,2,2,2,2,1,1 %N A382288 Number of records in the n-th composition in standard order. %C A382288 Here a record is a part of the composition that is greater than all parts before it, reading left to right. The first part of any nonempty composition is a record so a(n) >= 1 for n > 0. See A066099 for the standard order of integer compositions. %C A382288 The first appearance of k occurs at n = A164894(k) for k > 0. %F A382288 a(A164894(n)) = n for n > 0. %e A382288 The 883rd composition is (1, 2, 1, 1, 3, 1, 1) with records 1, 2, and 3; so a(883) = 3. %e A382288 ^ ^ ^ %o A382288 (Python) %o A382288 def comp(n): %o A382288 return # see A357625 %o A382288 def A382288(n): %o A382288 r,c = 0,0 %o A382288 for i in comp(n): %o A382288 if i > r: %o A382288 c += 1 %o A382288 r = i %o A382288 return c %Y A382288 Cf. A066099, A124762, A124767, A124768, A164894, A333381, A333382, A382312. %K A382288 nonn,easy %O A382288 0,7 %A A382288 _John Tyler Rascoe_, Mar 20 2025