A375244 List of triples {w;x;y} where «w» is the w-th «pyramid», "x" = the number of elements in the «pyramid» that are not erased (before the end-level erasure); "y" is the number of steps in the pyramid until the iteration stops. See the Comments section for more details.

1, 13, 12, 2, 12, 11, 3, 12, 10, 4, 11, 10, 5, 2, 4, 6, 11, 9, 7, 127, 79, 8, 10, 9, 9, 9, 7, 10, 1, 3, 11, 1, 2, 12, 10, 8, 13, 10, 8, 14, 126, 78, 15, 121, 77, 16, 9, 8, 17, 119, 75, 18, 8, 6, 19, 118, 74, 20, 1, 3, 21, 136, 76, 22, 1, 2, 23, 134, 75, 24, 120, 74, 25, 9, 9, 26, 121, 74, 27, 7, 8, 28, 116, 73

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Aug 07 2024

Keywords

• nonn
• base

Comments

Start the top of a "pyramid" with an integer w.

Form the lower level by adding w to each digit of w.

Erase any term having one or more duplicates, as well as its duplicates.

Iterate.

All "pyramids" will be blocked at some point, because their lowest level will end up completely erased.

Examples

			We start the first pyramid with w = 1:
.
                                 1
                                 2
                                 4
                                 8
                                16
                               17.22
                            18.24.24.24
             (a triple erasure, 22 will be erased later)
                               19.26
                            20.28.28.32
             (a double erasure, 20 will be erased later)
                            22.20.35.34
              (we erase now the 22-pair and the 20-pair)
                            38.40.37.38
      (a double erasure again, 40 will be erased at the next step)
                            44.40.40.44
.
The iteration stops there. w = 1, x = 13 as 13 terms were not erased in the blocked pyramid, y = 12 as the now blocked-pyramid has 12 levels.
Those numbers form the first triple of the sequence {1;13;12}.
		

Links

• Eric Angelini, This is not a fractal pipe, Personal blog of the author.

Crossrefs

Cf. A351330.