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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.

%I A375244 #17 Aug 11 2024 23:23:29
%S A375244 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,
%T A375244 10,1,3,11,1,2,12,10,8,13,10,8,14,126,78,15,121,77,16,9,8,17,119,75,
%U A375244 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
%N 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.
%C A375244 Start the top of a "pyramid" with an integer w.
%C A375244 Form the lower level by adding w to each digit of w.
%C A375244 Erase any term having one or more duplicates, as well as its duplicates.
%C A375244 Iterate.
%C A375244 All "pyramids" will be blocked at some point, because their lowest level will end up completely erased.
%H A375244 Eric Angelini, <a href="https://cinquantesignes.blogspot.com/2024/07/this-is-not-fractal-pipe.html">This is not a fractal pipe</a>, Personal blog of the author.
%e A375244 We start the first pyramid with w = 1:
%e A375244 .
%e A375244                                  1
%e A375244                                  2
%e A375244                                  4
%e A375244                                  8
%e A375244                                 16
%e A375244                                17.22
%e A375244                             18.24.24.24
%e A375244              (a triple erasure, 22 will be erased later)
%e A375244                                19.26
%e A375244                             20.28.28.32
%e A375244              (a double erasure, 20 will be erased later)
%e A375244                             22.20.35.34
%e A375244               (we erase now the 22-pair and the 20-pair)
%e A375244                             38.40.37.38
%e A375244       (a double erasure again, 40 will be erased at the next step)
%e A375244                             44.40.40.44
%e A375244 .
%e A375244 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.
%e A375244 Those numbers form the first triple of the sequence {1;13;12}.
%Y A375244 Cf. A351330.
%K A375244 nonn,base
%O A375244 1,2
%A A375244 _Eric Angelini_ and _Jean-Marc Falcoz_, Aug 07 2024