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A288774 a(n) is the largest positive integers whose partitions into consecutive parts can be totally represented in the first n rows of the table described in A286000.

%I A288774 #11 Oct 21 2017 21:07:31
%S A288774 1,2,2,4,4,5,5,8,8,8,9,11,11
%N A288774 a(n) is the largest positive integers whose partitions into consecutive parts can be totally represented in the first n rows of the table described in A286000.
%C A288774 a(n) has the same definition related to the table A286001 which is another version of the table A286000.
%C A288774 First differs from A288773 at a(12), which shares infinitely many terms.
%e A288774 Figures A, B, C show the evolution of the table of partitions into consecutive parts described in A286000, with 11, 12 and 13 rows respectively:
%e A288774 .     -----------------------------------------------------
%e A288774 Figure:       A                B                 C
%e A288774 -----------------------------------------------------------
%e A288774 .   n =      11               12                13
%e A288774 Row   -----------------------------------------------------
%e A288774 1     |  1;            |   1;           |   1;            |
%e A288774 1     |  2;            |   2;           |   2;            |
%e A288774 3     |  3,  2;        |   3,  2;       |   3,  2;        |
%e A288774 4     |  4,  1;        |   4,  1;       |   4,  1;        |
%e A288774 5     |  5,  3;        |   5,  3;       |   5,  3;        |
%e A288774 6     |  6,  2,  3;    |   6,  2,  3;   |   6,  2,  3;    |
%e A288774 7     |  7,  4,  2;    |   7,  4,  2;   |   7,  4,  2;    |
%e A288774 8     |  8,  3,  1;    |   8,  3,  1;   |   8,  3,  1;    |
%e A288774 9     | [9],[5],[4];   |   9,  5,  4;   |   9,  5,  4;    |
%e A288774 10    | 10, [4],[3], 4;|  10,  4,  3, 4;|  10,  4,  3;  4;|
%e A288774 11    | 11,  6, [2], 3;| [11],[6], 2; 3;| [11],[6], 2,  3;|
%e A288774 12    |                |  12, [5], 5, 2;|  12, [5], 5,  2;|
%e A288774 13    |                |                |  13,  7,  4,  1;|
%e A288774 .     -----------------------------------------------------
%e A288774 . a(n):       9                11                 11
%e A288774 .     -----------------------------------------------------
%e A288774 For n = 11, in the first 11 rows of the table can be represented the partitions into consecutive parts of the integers 1, 2, 3, 4, 5, 6, 7, 8 and 9. The largest of these positive integers is 9, so a(11) = 9.
%e A288774 For n = 12, in the first 12 rows of the table can be represented the partitions into consecutive parts of the integers 1, 2, 3, 4, 5, 6, 7, 8, 9 and 11. The largest of these positive integers is 11, so a(12) = 11.
%e A288774 For n = 13, in the first 13 rows of the table can be represented the partitions into consecutive parts of the integers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11. The largest of these positive integers is 11, so a(13) = 11.
%Y A288774 Cf. A237593, A286000, A286001, A288529, A288772, A288773.
%K A288774 nonn,more
%O A288774 1,2
%A A288774 _Omar E. Pol_, Jun 22 2017