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%I #11 Dec 02 2019 04:14:30
%S 1,2,3,4,5,6,7,8,9,10,11,20,12,30,13,22,21,33,23,10,24,14,25,15,26,16,
%T 27,17,28,18,29,19,32,31,40,34,11,20,35,36,12,30,41,42,13,22,37,38,21,
%U 33,44,43,50,45,23,10,24,39,49,51,52,14,25,46,47,15,26,48,54,16,27,53,55,17,28
%N A fractal-like sequence: erasing all pairs of consecutive terms that have at least one digit in common leaves the sequence unchanged.
%C The sequence is fractal-like as it embeds an infinite number of copies of itself.
%C The sequence was built according to these rules (see, in the Example section, the parenthesization technique):
%C 1) no overlapping pairs of parentheses;
%C 2) always start the content inside a pair of parentheses with the smallest integer S > 9 not yet present inside another pair of parentheses;
%C 3) always end the content inside a pair of parentheses with the smallest integer H > 9 not yet present inside another pair of parentheses such that the integers S and H have at least one digit in common;
%C 4) after a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 4, a(5) = 5, a(6) = 6, a(7) = 7, a(8) = 8, a(9) = 9, a(10) = 10, always try to extend the sequence with a duplicate > 9 of the oldest term of the sequence not yet duplicated; if this leads to a contradiction, open a new pair of parentheses;
%C 5) Never use a term of A171102 (Pandigital numbers: numbers containing the digits 0-9. Version 2: each digit appears at least once).
%H Lars Blomberg, <a href="/A303948/b303948.txt">Table of n, a(n) for n = 1..10000</a>
%e Parentheses are added around each pair of terms having at least one digit in common:
%e 1,2,3,4,5,6,7,8,9,(10,11),(20,12),(30,13),(22,21),(33,23),10,(24,14),(25,15),(26,16),(27,17),(28,18),(29,19),(32,31),(40,34),11,20,(35,36),12,30,(41,42),13,
%e Erasing all the parenthesized contents yields
%e 1,2,3,4,5,6,7,8,9,(.....),(.....),(.....),(.....),(.....),10,(.....),(.....),(.....),(.....),(.....),(.....),(.....),(.....),11,20,(.....),12,30,(.....),13,
%e We see that the remaining terms slowly rebuild the starting sequence.
%Y Cf. A303845 for another "erasing criterion" (prime by concatenation).
%K nonn,base
%O 1,2
%A _Eric Angelini_ and _Lars Blomberg_, May 03 2018
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