[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, ...
http://www.cetteadressecomportecinquantesignes.com/RightTriangleNumbers.htm
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