A380587 Split A377091 into sublists consisting of runs of terms with the same sign. Then a(n) is the maximum value of the first differences of the absolute value of the terms within the n-th sublist.

1, -1, 1, -1, 1, 4, 1, 1, 1, 1, 4, 1, 4, 4, 1, 1, 1, 1, 1, 4, 1, 4, 4, 1, 4, 1, 4, 1, 1, 1, 1, 1, 4, 4, 1, 4, 1, 4, 1, 4, 1, 4, 4, 4, 4, 4, 4, 4, 9, 4, 9, 4, 4, 4, 9, 4, 4, 4, -1, 4, 9, -1, 1, 1, 4, 1, 4, -1, 4, 4, 4, 9, 1, 4, 9, 4, 9, 9, -1, 1, 1, 9, -1, 1, 4, 4, 1, 4, 1, 4

Offset

2,6

Comments

The first sublist is ignored, since it has length 1 (see Example).

By considering terms in A377091 up to n = 10^6 (2030 sublists), a(n) = -1, 1, 4 or 9.

Links

Paolo Xausa, Table of n, a(n) for n = 2..2000

Example

A377091 with terms grouped by sign begins:
  (0) (1 2) (-2 -1) (3 4 5) (-4 -3) (6 7 8) (-8 -7 -6 -5 -9 -10 -11 -12) ...
Their absolute value is:
  (0) (1 2) ( 2  1) (3 4 5) ( 4  3) (6 7 8) ( 8  7  6  5  9  10  11  12) ...
Their first differences are (we ignore the first sublist):
      (1  ) (-1   ) (1 1  ) (-1   ) (1 1  ) (-1 -1 -1  4  1   1   1    ) ...
And the corresponding terms of the present sequence are therefore:
       1     -1      1       -1      1        4 ...

Mathematica

(* A377091list is defined at A377091 *)
Map[Max[Differences[Abs[#]]] &, SplitBy[A377091list[2000], Sign][[2 ;; -2]]]

Crossrefs

Cf. A377091, A379882, A380510, A380586, A380588.

Sequence in context: A388188 A196879 A193349 * A053231 A379545 A066701

Adjacent sequences: A380584 A380585 A380586 * A380588 A380589 A380590

Keyword

sign

Author

Paolo Xausa, Jan 27 2025

Status

approved