[seqfan] Integers shaped like right triangles

Eric Angelini Eric.Angelini at kntv.be
Tue Nov 30 15:46:24 CET 2010

```Hello Seqfans,
if the hereunder sequence is of interest, please let me know
and I'll submit it to the OEIS (computed by hand, though).
Best,
É.
[this has been posted on Math-Fun a couple of days ago]
-------------------------------------------------------

> Hello Math-Fun,

Write an integer somewhere on a grid, one digit per square:
+---+---+---+---+---+---+
|   |   |   |   |   |   |
+---+---+---+---+---+---+
|   |   |   |   |   |   |
+---+---+---+---+---+---+
|   | 1 | 3 | 4 | 0 |   |
+---+---+---+---+---+---+
|   |   |   |   |   |   |
+---+---+---+---+---+---+
|   |   |   |   |   |   |
+---+---+---+---+---+---+
|   |   |   |   |   |   |
+---+---+---+---+---+---+

The digits will now move vertically:
- odd digit j will climb j squares
- even digit k will sink k squares
- zero stays were it is

In our example, the digits of 1340 move like this:
+---+---+---+---+
|   | 3 |   |   |
+---+---+---+---+
|   |   |   |   |
+---+---+---+---+
| 1 |   |   |   |
+---+---+---+---+
| . | . | . | 0 |
+---+---+---+---+
|   |   |   |   |
+---+---+---+---+
|   |   |   |   |
+---+---+---+---+
|   |   |   |   |
+---+---+---+---+
|   |   | 4 |   |
+---+---+---+---+

Encircle now those new digits with an elastic band. The resulting shape is not a right triangle - which is a pity because we are precisely looking for integers moving into right triangles! The additional constraint being that ALL the new digits must be ON the elastic band.

S = 101, 103, 120, 130, 210, 301, 1032, 1307, 2301, 3210, 6120, 7031, 10325, 11311, 13079, 19753, 22022, 22422, 24680, 33133, 33533, 35791, 43210, 44244, 44644, 52301, 55355, 55755, 64208, 66466, 66866, 75319, 77577, 77977, 80246, 86120, 88688, 91357, 97031, 99799, ...