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.

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?

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10012

Rémy Sigrist, C++ program for A329724

Rémy Sigrist, Scatterplot of the first 39582754 terms

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

Cf. A000124, A001057.

Sequence in context: A143329 A365227 A053440 * A143332 A255919 A212189

Adjacent sequences: A329721 A329722 A329723 * A329725 A329726 A329727

Keyword

sign,look

Author

Rémy Sigrist, Nov 19 2019

Status

approved