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A329724
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Sequence of distinct integers such that a(1) = 0, and for k = 1, 2, ..., the last term so far and the k next terms are in arithmetic progression with common difference d_k such that abs(d_k) is as small as possible and d_k > 0 iff k is odd.
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1
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0, 1, -1, -3, 2, 7, 12, 11, 10, 9, 8, 13, 18, 23, 28, 33, 19, 5, -9, -23, -37, -51, -50, -49, -48, -47, -46, -45, -44, -52, -60, -68, -76, -84, -92, -100, -108, -83, -58, -33, -8, 17, 42, 67, 92, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 118, 129
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OFFSET
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1,4
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COMMENTS
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The sequence zigzags and A000124 corresponds to the indices of its extrema.
Will this sequence change sign infinitely often?
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LINKS
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EXAMPLE
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The first terms, alongside the corresponding k and d_k, are:
n a(n) k d_k
-- ---- --- ---
1 0 N/A N/A
2 1 1 1
3 -1 2 -2
4 -3 2 -2
5 2 3 5
6 7 3 5
7 12 3 5
8 11 4 -1
9 10 4 -1
10 9 4 -1
11 8 4 -1
12 13 5 5
13 18 5 5
14 23 5 5
15 28 5 5
16 33 5 5
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PROG
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(C++) See Links section.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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