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A329724
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.
1
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
OFFSET
1,4
COMMENTS
The sequence zigzags and A000124 corresponds to the indices of its extrema.
Will this sequence change sign infinitely often?
EXAMPLE
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
PROG
(C++) See Links section.
CROSSREFS
Sequence in context: A143329 A365227 A053440 * A143332 A255919 A212189
KEYWORD
sign,look
AUTHOR
Rémy Sigrist, Nov 19 2019
STATUS
approved