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A300019
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For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shows at least a digit 5.
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1
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5, 10, 20, 15, 1, 2, 3, 9, 30, 40, 16, 4, 50, 45, 6, 19, 60, 17, 7, 26, 65, 8, 27, 18, 11, 12, 13, 14, 21, 22, 29, 25, 35, 66, 24, 70, 80, 28, 32, 67, 23, 75, 55, 46, 34, 68, 42, 56, 44, 31, 33, 36, 57, 43, 58, 52, 47, 53, 48, 62, 37, 63, 38, 72, 90, 39, 41, 59, 49, 51, 61, 100, 110, 120, 105, 85, 115, 95, 106, 54, 64, 76, 107, 73, 125, 101, 74, 126, 84, 116, 69, 71, 94, 130
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OFFSET
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1,1
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COMMENTS
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The sequence starts with a(1) = 5 and is always extended with the smallest integer not yet present that does not lead to a contradiction.
A permutation of the natural numbers
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LINKS
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EXAMPLE
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5 shows a digit 5, of course (k = 1)
5 + 10 = 15 and 15 shows at least a digit 5 (k = 2)
5 + 10 + 20 = 35 and 35 shows at least a digit 5 (k = 3)
5 + 10 + 20 + 15 = 50 and 50 shows at least a digit 5 (k = 4)
5 + 10 + 20 + 15 + 1 = 51 and 51 shows at least a digit 5 (k = 5)
5 + 10 + 20 + 15 + 1 + 2 = 53 and 53 shows at least a digit 5 (k = 6)
...
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CROSSREFS
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Cf. A300015 (which is the lexicographic first sequence of positive integers without duplicate terms having this property).
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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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