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 A288772 #27 Oct 21 2017 21:06:32 %S A288772 1,2,4,4,6,8,8,8,11,13,13,14,14,17,19,19,19,21,21,24,26,26,26,26,29, %T A288772 29,32,34,34,34,34,34,38,38,41,43,43,43,44,44,44,48,48,51,53,53,53,53, %U A288772 55,55,56,59,59,62,64,64,64,64,64,67,67,67,71,71,74,76,76,76,76,76,76,80,80,80,84,84,87,89,89,89,89 %N A288772 a(n) is the minimum number of rows from the table described in A286000 that are required to represent the partitions of all positive integers <= n into consecutive parts. %C A288772 a(n) has the same definition related to the table A286001 which is another version of the table A286000. %C A288772 First differs from A288529 at a(11), which shares infinitely many terms. %e A288772 Figures A..D show the evolution of the table of partitions into consecutive parts described in A286000, for n = 8..11: %e A288772 . --------------------------------------------------------------------- %e A288772 Figure: A B C D %e A288772 . --------------------------------------------------------------------- %e A288772 . n: 8 9 10 11 %e A288772 Row --------------------------------------------------------------------- %e A288772 1 | 1; | 1; | 1; | 1; | %e A288772 1 | 2; | 2; | 2; | 2; | %e A288772 3 | 3, 2; | 3, 2; | 3, 2; | 3, 2; | %e A288772 4 | 4, 1; | 4, 1; | 4, 1; | 4, 1; | %e A288772 5 | 5, 3; | 5, 3; | 5, 3; | 5, 3; | %e A288772 6 | 6, 2, 3;| 6, 2, 3; | 6, 2, 3; | 6, 2, 3; | %e A288772 7 | 7, 4, 2;| 7, 4, 2; | 7, 4, 2; | 7, 4, 2; | %e A288772 8 | [8], 3, 1;| 8, 3, 1; | 8, 3, 1; | 8, 3, 1; | %e A288772 9 | | [9],[5],[4]; | 9, 5, 4; | 9, 5, 4; | %e A288772 10 | | 10, [4],[3], 4;| [10], 4, 3, [4];| 10, 4, 3; 4;| %e A288772 11 | | 11, 6, [2], 3;| 11, 6, 2; [3];| [11],[6], 2, 3;| %e A288772 12 | | | 12, 5, 5, [2];| 12, [5], 5, 2;| %e A288772 13 | | | 13, 7, 4, [1];| 13, 7, 4, 1;| %e A288772 . --------------------------------------------------------------------- %e A288772 . a(n): 8 11 13 13 %e A288772 . --------------------------------------------------------------------- %e A288772 For n = 8 we need a table with at least 8 rows, so a(8) = 8. %e A288772 For n = 9 we need a table with at least 11 rows, so a(9) = 11. %e A288772 For n = 10 we need a table with at least 13 rows, so a(10) = 13. %e A288772 For n = 11 we need a table with at least 13 rows, so a(11) = 13. %Y A288772 Cf. A001227, A109814, A204217, A237593, A286000, A286001, A288529, A288773, A288774. %K A288772 nonn %O A288772 1,2 %A A288772 _Omar E. Pol_, Jun 17 2017