OFFSET
1,2
COMMENTS
The sequence is fractal-like as it contains an infinite number of copies of itself.
The sequence was built according to these rules (see, in the Example section, the parenthesization technique):
1) no overlapping pairs of parentheses;
2) always start the content inside a pair of parentheses with the smallest integer S > 10 not yet present inside another pair of parentheses;
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;
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.
LINKS
Eric Angelini, Table of n, a(n) for n = 1..585
EXAMPLE
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):
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,
Erasing all the parenthesized contents yields
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,
We see that the remaining terms slowly rebuild the starting sequence.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Eric Angelini, May 08 2018
STATUS
approved