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A303948
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A fractal-like sequence: erasing all pairs of consecutive terms that have at least one digit in common leaves the sequence unchanged.
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12
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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, 22, 37, 38, 21, 33, 44, 43, 50, 45, 23, 10, 24, 39, 49, 51, 52, 14, 25, 46, 47, 15, 26, 48, 54, 16, 27, 53, 55, 17, 28
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OFFSET
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1,2
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COMMENTS
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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).
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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Cf. A303845 for another "erasing criterion" (prime by concatenation).
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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