A302389 A fractal-like sequence: erasing all pairs of contiguous terms that don't have a digit in common leaves the sequence unchanged.

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, 34, 26, 27, 35, 5, 15, 41, 28, 29, 36, 6, 16, 46, 37, 7, 17, 47, 38, 8, 18, 48, 39, 9, 19, 49, 50, 20, 10, 51, 42, 22, 21, 52

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 X > 1 not yet present inside another pair of parentheses;

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;

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.

Links

Lars Blomberg, Table of n, a(n) for n = 1..998

Example

Parentheses are added around each pair of terms that have no digit in common:
(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,
Erasing all the parenthesized contents yields
(...),(....),(....),(....),(....),(....),(....),(....),(.....),(.....),(.....),(.....),1,( .....),2,12,( .....),3,13,( .....),4,14,
We see that the remaining terms slowly rebuild the starting sequence.

Crossrefs

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

Sequence in context: A371589 A082827 A290100 * A072484 A337918 A113698

Adjacent sequences: A302386 A302387 A302388 * A302390 A302391 A302392

Keyword

nonn,base

Author

Eric Angelini and Lars Blomberg, May 03 2018

Status

approved