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

1,2

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.

Links

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A073409 A260234 A151548 * A177433 A264827 A214091

Adjacent sequences: A256255 A256256 A256257 * A256259 A256260 A256261

Keyword

nonn,tabf

Author

Omar E. Pol, Apr 04 2015

Status

approved