A256258 Triangle read by rows in which the row lengths are the terms of A011782 and row n lists the terms of A016969 except for the right border which gives the positive terms of A000225.

1, 3, 5, 7, 5, 11, 17, 15, 5, 11, 17, 23, 29, 35, 41, 31, 5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71, 77, 83, 89, 63, 5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71, 77, 83, 89, 95, 101, 107, 113, 119, 125, 131, 137, 143, 149, 155, 161, 167, 173, 179, 185, 127, 5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71, 77, 83, 89, 95, 101, 107, 113, 119, 125, 131, 137

Offset: 1

Author

Omar E. Pol, Apr 04 2015

Keywords

• nonn
• tabf

Comments

Row sums give A002001.

The sum of all terms of first n rows gives A000302(n-1).

The rows of triangle A256263 converge to this sequence.

Rows converge to A016969.

First 11 terms agree with A151548.

Examples

			Written as an irregular triangle in which the row lengths are the terms of A011782, the sequence begins:
1;
3;
5,7;
5,11,17,15;
5,11,17,23,29,35,41,31;
5,11,17,23,29,35,41,47,53,59,65,71,77,83,89,63;
5,11,17,23,29,35,41,47,53,59,65,71,77,83,89,95,101,107,113,119,125,131,137,143,149,155,161,167,173,179,185,127;
...
Illustration of initial terms in the fourth quadrant of the square grid:
------------------------------------------------------------------------
n   a(n)             Compact diagram
------------------------------------------------------------------------
.            _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
1    1      |_| | | |_ _  | |_ _ _ _ _ _  | |
2    3      |_ _| | |_  | | |_ _ _ _ _  | | |
3    5      |_ _ _| | | | | |_ _ _ _  | | | |
4    7      |_ _ _ _| | | | |_ _ _  | | | | |
5    5      | | |_ _ _| | | |_ _  | | | | | |
6   11      | |_ _ _ _ _| | |_  | | | | | | |
7   17      |_ _ _ _ _ _ _| | | | | | | | | |
8   15      |_ _ _ _ _ _ _ _| | | | | | | | |
9    5      | | | | | | |_ _ _| | | | | | | |
10  11      | | | | | |_ _ _ _ _| | | | | | |
11  17      | | | | |_ _ _ _ _ _ _| | | | | |
12  23      | | | |_ _ _ _ _ _ _ _ _| | | | |
13  29      | | |_ _ _ _ _ _ _ _ _ _ _| | | |
14  35      | |_ _ _ _ _ _ _ _ _ _ _ _ _| | |
15  41      |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |
16  31      |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
.
a(n) is also the number of cells in the n-th region of the diagram.
It appears that A241717 can be represented by a similar diagram.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..8192

Crossrefs

Cf. A000225, A000302, A002001, A011782, A016969, A141548, A241717, A256260, A256261, A256263, A256264.

Programs

Mathematica

Nest[Join[#, Range[Length[#] - 1]*6 - 1, {2 #[[-1]] + 1}] &, {1}, 7] (* Ivan Neretin, Feb 14 2017 *)