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A302389 A fractal-like sequence: erasing all pairs of contiguous terms that don't have a digit in common leaves the sequence unchanged. 7
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 (list; graph; refs; listen; history; text; internal format)
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: A012629 A082827 A290100 * A072484 A113698 A048794

Adjacent sequences:  A302386 A302387 A302388 * A302390 A302391 A302392

KEYWORD

nonn,base,changed

AUTHOR

Eric Angelini and Lars Blomberg, May 03 2018

STATUS

approved

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Last modified December 13 22:55 EST 2019. Contains 329974 sequences. (Running on oeis4.)