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

1,2

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.

Links

Table of n, a(n) for n=1..84.

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

Example

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}.

Crossrefs

Cf. A351330.

Sequence in context: A083229 A140554 A356978 * A022969 A023455 A055124

Adjacent sequences: A375241 A375242 A375243 * A375245 A375246 A375247

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Aug 07 2024

Status

approved