A288773 a(n) is the largest of all positive integers whose partitions into consecutive parts can be totally represented in the first n rows of the table described in A286000.

1, 2, 2, 4, 4, 5, 5, 8, 8, 8, 9, 9, 11

Offset

1,2

Comments

a(n) has the same definition related to the table A286001 which is another version of the table A286000.

First differs from A288774 at a(12), which shares infinitely many terms.

Links

Table of n, a(n) for n=1..13.

Example

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:
.     ------------------------------------------------------
Figure:       A                B                  C
------------------------------------------------------------
.   n =      11               12                 13
Row   ------------------------------------------------------
1     |  1;            |   1;            |   1;            |
1     |  2;            |   2;            |   2;            |
3     |  3,  2;        |   3,  2;        |   3,  2;        |
4     |  4,  1;        |   4,  1;        |   4,  1;        |
5     |  5,  3;        |   5,  3;        |   5,  3;        |
6     |  6,  2,  3;    |   6,  2,  3;    |   6,  2,  3;    |
7     |  7,  4,  2;    |   7,  4,  2;    |   7,  4,  2;    |
8     |  8,  3,  1;    |   8,  3,  1;    |   8,  3,  1;    |
9     | [9],[5],[4];   |  [9],[5],[4];   |   9,  5,  4;    |
10    | 10, [4],[3], 4;|  10, [4],[3], 4;|  10,  4,  3;  4;|
11    | 11,  6, [2], 3;|  11,  6, [2]; 3;| [11],[6], 2,  3;|
12    |                |  12,  5,  5,  2;|  12, [5], 5,  2;|
13    |                |                 |  13,  7,  4,  1;|
.     ------------------------------------------------------
. a(n):       9                 9                 11
.     ------------------------------------------------------
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.
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, but the partitions into consecutive parts of 10 cannot be represented, so a(12) = 9, not 11.
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.

Crossrefs

Cf. A237593, A286000, A286001, A288529, A288772, A288774.

Sequence in context: A260734 A265428 A035644 * A288774 A113474 A089413

Adjacent sequences: A288770 A288771 A288772 * A288774 A288775 A288776

Keyword

nonn,more

Author

Omar E. Pol, Jun 17 2017

Status

approved