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A335492
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The successive absolute differences between two digits are the successive absolute differences between two terms.
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2
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 17, 11, 17, 17, 17, 23, 29, 35, 41, 47, 42, 43, 44, 37, 31, 33, 32, 35, 38, 41, 44, 46, 48, 49, 50, 50, 51, 55, 59, 57, 59, 59, 59, 58, 59, 61, 63, 68, 64, 67, 70, 70, 70, 72, 74, 78, 82, 77, 73, 78, 83, 88, 93, 89, 85, 85, 85, 81, 85, 87, 89, 93, 97, 101, 105, 109, 113, 110
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OFFSET
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1,3
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COMMENTS
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To extend the sequence S with a new term a(n), we always try to subtract from a(n-1) the last absolute difference D between two digits that we must consider. If a(n) is already in S, we add D to a(n-1) instead of subtracting, even if this new a(n) is already in S.
Note that a(n) is sometimes < a(n-1).
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LINKS
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EXAMPLE
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After a(10) = 9, we cannot extend S with a(11) < 17 as the difference between a(10) and a(11) cannot be < 8, this 8 being the difference between 9 and the first digit of a(11);
After a(11) = 17, we are driven by the next absolute difference between digits, which is 6 (the difference between the 1 and the 7 of 17). As a(11) - 6 = 11 and this 11 is not yet in S, we keep this 11 as a(12);
After a(12) = 11, the next absolute difference between two digits that we must consider is 6 again (this 6 comes from the difference between the 7 of 17 and the first 1 of 11); but as a(12) = 11 and 11 - 6 is 5, we won't accept this 5 for a(13) as 5 is already in S; we then add 6 to a(12) instead of subtracting, and we produce another 17 in S (this is allowed as we are adding an absolute difference, not subtracting). So a(13) is now 17;
After a(13) = 17, the next absolute difference between two digits that we must consider is 0 (this 0 comes from the difference between the two 1s of 11); so a(14) = 17; etc.
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CROSSREFS
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Cf. A335493 [same idea but a(n) is never < a(n-1)].
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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