A302389 - OEIS

%I #39 Dec 02 2019 04:11:28

%S 1,2,12,3,13,4,14,5,15,6,16,7,17,8,18,9,19,20,10,22,21,30,23,11,1,31,

%T 24,2,12,25,33,3,13,32,40,4,14,34,26,27,35,5,15,41,28,29,36,6,16,46,

%U 37,7,17,47,38,8,18,48,39,9,19,49,50,20,10,51,42,22,21,52

%N A fractal-like sequence: erasing all pairs of contiguous terms that don't have a 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 X > 1 not yet present inside another pair of parentheses;

%C   3) always end the content inside a pair of parentheses with the smallest integer Y > 1 not yet present inside another pair of parentheses such that X and Y have no digit in common;

%C   4) after a(1) = 1 and a(2) = 2, always try to extend the sequence with a duplicate > 2 of the oldest term of the sequence not yet duplicated; if this leads to a contradiction, open a new pair of parentheses.

%H Lars Blomberg, <a href="/A302389/b302389.txt">Table of n, a(n) for n = 1..998</a>

%e Parentheses are added around each pair of terms that have no digit in common:

%e (1,2),(12,3),(13,4),(14,5),(15,6),(16,7),(17,8),(18,9),(19,20),(10,22),(21,30),(23,11),1,(31,24),2,12,(25,33),3,13,(32,40),4,14,

%e Erasing all the parenthesized contents yields

%e (...),(....),(....),(....),(....),(....),(....),(....),(.....),(.....),(.....),(.....),1,( .....),2,12,( .....),3,13,( .....),4,14,

%e We see that the remaining terms slowly rebuild the starting sequence.

%Y For other erasing criteria, cf. A303845 (prime by concatenation), A303948 (pair sharing a digit), A274329 (pair summing up to a prime).

%K nonn,base

%O 1,2

%A _Eric Angelini_ and _Lars Blomberg_, May 03 2018