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A300015
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For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shows at least a digit 1. Lexicographic first sequence of positive integers without duplicate terms having this property.
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10
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1, 9, 2, 3, 4, 12, 10, 20, 30, 11, 5, 6, 7, 8, 13, 14, 15, 16, 24, 21, 40, 39, 31, 50, 19, 41, 59, 51, 49, 61, 42, 18, 60, 22, 28, 69, 71, 23, 17, 25, 26, 27, 29, 32, 33, 34, 35, 36, 37, 38, 43, 44, 45, 46, 47, 48, 52, 53, 54, 55, 56, 57, 58, 70, 62, 68, 79, 81, 80, 90, 100, 110, 120, 119
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OFFSET
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1,2
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COMMENTS
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The sequence starts with a(1) = 1 and is always extended with the smallest integer not yet present that does not lead to a contradiction.
A permutation of the natural numbers.
A fractal structure arises when considering the sequence b defined by b(n) = a(n) - n at different scales. - Rémy Sigrist, Feb 19 2019
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LINKS
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EXAMPLE
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1 shows a digit 1, of course (k = 1)
1 + 9 = 10 and 10 shows at least a digit 1 (k = 2)
1 + 9 + 2 = 12 and 12 shows at least a digit 1 (k = 3)
1 + 9 + 2 + 3 = 15 and 15 shows at least a digit 1 (k = 4)
1 + 9 + 2 + 3 + 4 = 19 and 19 shows at least a digit 1 (k = 5)
1 + 9 + 2 + 3 + 4 + 12 = 31 and 31 shows at least a digit 1 (k = 6)
...
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CROSSREFS
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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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