OFFSET
1,2
COMMENTS
The sequence is fractal-like as it embeds 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 > 9 not yet present inside another pair of parentheses;
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;
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;
5) Never use a term of A171102 (Pandigital numbers: numbers containing the digits 0-9. Version 2: each digit appears at least once).
LINKS
Lars Blomberg, Table of n, a(n) for n = 1..10000
EXAMPLE
Parentheses are added around each pair of terms having at least one digit in common:
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,
Erasing all the parenthesized contents yields
1,2,3,4,5,6,7,8,9,(.....),(.....),(.....),(.....),(.....),10,(.....),(.....),(.....),(.....),(.....),(.....),(.....),(.....),11,20,(.....),12,30,(.....),13,
We see that the remaining terms slowly rebuild the starting sequence.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Eric Angelini and Lars Blomberg, May 03 2018
STATUS
approved