A304232 - OEIS

%I #10 Jun 03 2018 16:48:05

%S 1,2,3,4,5,6,7,8,9,10,11,12,11,21,13,12,11,21,22,20,13,12,11,21,22,14,

%T 40,20,13,12,11,21,22,14,15,50,40,20,13,12,11,21,22,14,15,16,60,50,40,

%U 20,13,12,11,21,22,14,15,16,17,70,60,50,40,20,13,12,11,21,22,14,15,16,17,18,80

%N A fractal-like sequence: erasing all pairs of consecutive terms a(n) and a(n+1) having the property that the last digit of a(n) is the same as the first digit of a(n+1) leaves the sequence unchanged.

%C The sequence is fractal-like as it contains 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 > 10 not yet present inside another pair of parentheses;

%C   3) always end the content inside a pair of parentheses with the smallest integer T > 10 not yet present inside another pair of parentheses such that the integer S ends with a digit d and the integer T starts with the same digit d;

%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 > 10 of the oldest term of the sequence not yet duplicated; if this leads to a contradiction, open a new pair of parentheses.

%H Eric Angelini, <a href="/A304232/b304232.txt">Table of n, a(n) for n = 1..585</a>

%e Parentheses are added around each pair of terms such that the last digit of a(n) is the same as the first digit of a(n+1):

%e 1,2,3,4,5,6,7,8,9,10,(11,12),11,(21,13),12,11,21,(22,20),13,12,11,21,22,(14,40),20,13,12,11,21,22,14,(15,50),40,20,

%e Erasing all the parenthesized contents yields

%e 1,2,3,4,5,6,7,8,9,10,(.....),11,(.....),12,11,21,(.....),13,12,11,21,22,(.....),20,13,12,11,21,22,14,(.....),40,20,

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

%Y Cf. A303845 or A303948 (where the erasure techniques are different).

%K nonn,base

%O 1,2

%A _Eric Angelini_, May 08 2018