A261348 a(1)=0; a(2)=0; for n>2: a(n) = A237591(n,2) = A237593(n,2).

0, 0, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2, 3, 3, 3, 3, 4, 3, 4, 4, 4, 4, 5, 4, 5, 5, 5, 5, 6, 5, 6, 6, 6, 6, 7, 6, 7, 7, 7, 7, 8, 7, 8, 8, 8, 8, 9, 8, 9, 9, 9, 9, 10, 9, 10, 10, 10, 10, 11, 10, 11, 11, 11, 11, 12, 11, 12, 12, 12, 12, 13, 12, 13, 13, 13, 13, 14, 13, 14, 14, 14, 14, 15, 14, 15, 15, 15, 15, 16, 15, 16, 16, 16, 16, 17, 16

Offset

1,5

Comments

n is an odd prime if and only if a(n) = 1 + a(n-1) and A237591(n,k) = A237591(n-1,k) for the values of k distinct of 2.

For k > 1 there are five numbers k in the sequence.

For more information see A237593.

Links

Table of n, a(n) for n=1..96.

Example

Apart from the initial two zeros the sequence can be written as an array T(j,k) with 6 columns, where row j is [j, j, j+1, j, j+1, j+1], as shown below:
1,   1,  2,  1,  2,  2;
2,   2,  3,  2,  3,  3;
3,   3,  4,  3,  4,  4;
4,   4,  5,  4,  5,  5;
5,   5,  6,  5,  6,  6;
6,   6,  7,  6,  7,  7;
7,   7,  8,  7,  8,  8;
8,   8,  9,  8,  9,  9;
9,   9, 10,  9, 10, 10;
10, 10, 11, 10, 11, 11;
11, 11, 12, 11, 12, 12;
12, 12, 13, 12, 13, 13;
13, 13, 14, 13, 14, 14;
14, 14, 15, 14, 15, 15;
15, 15, 16, 15, 16, 16;
...
Illustration of initial terms:
Row                                                     _
1                                                     _| |0
2                                                   _|  _|0
3                                                 _|   |1|
4                                               _|    _|1|
5                                             _|     |2 _|
6                                           _|      _|1| |
7                                         _|       |2  | |
8                                       _|        _|2 _| |
9                                     _|         |2  |  _|
10                                  _|          _|2  | | |
11                                _|           |3   _| | |
12                              _|            _|2  |   | |
13                            _|             |3    |  _| |
14                          _|              _|3   _| |  _|
15                        _|               |3    |   | | |
16                      _|                _|3    |   | | |
17                    _|                 |4     _|  _| | |
18                  _|                  _|3    |   |   | |
19                _|                   |4      |   |  _| |
20              _|                    _|4     _|   | |  _|
21            _|                     |4      |    _| | | |
22          _|                      _|4      |   |   | | |
23        _|                       |5       _|   |   | | |
24      _|                        _|4      |     |  _| | |
25    _|                         |5        |    _| |   | |
26   |                           |5        |   |   |   | |
...
The figure represents the triangle A237591 in which the numbers of horizontal cells in the second geometric region gives this sequence, for n > 2.
Note that this is also the second geometric region in the front view of the stepped pyramid described in A245092. For more information see also A237593.

Crossrefs

Cf. A000040, A236104, A235791, A237048, A237591, A237593, A261350, A261699.

Sequence in context: A008615 A103221 A026806 * A320536 A347698 A338336

Adjacent sequences: A261345 A261346 A261347 * A261349 A261350 A261351

Keyword

nonn,tabf,easy

Author

Omar E. Pol, Aug 24 2015

Status

approved