A380586 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 sorted terms within the n-th sublist.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 3, 2, 2, 2, 3, 2, 2, 4, 2, 1, 3, 4, 1, 3, 1, 2, 1, 2, 1, 2, 2, 3, 2, 1, 3, 4, 2, 3, 4, 1, 3, 1, 3, 1, 1, 4, 1, 1, 1, 1, 1

Offset

2,44

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, 2, 3 or 4.

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) ...
Sorted terms within groups are:
  (0) (1 2) (-2 -1) (3 4 5) (-4 -3) (6 7 8) (-12 -11 -10 -9 -8 -7 -6 -5) ...
Their first differences are (we ignore the first sublist):
      (1  ) ( 1   ) (1 1  ) ( 1   ) (1 1  ) (  1   1   1  1  1  1  1   ) ...
And the corresponding terms of the present sequence are therefore:
       1      1      1        1      1         1 ...

Mathematica

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

Crossrefs

Cf. A377091, A379882, A380510, A380587, A380588.

Sequence in context: A007723 A067437 A242425 * A263104 A282518 A230241

Adjacent sequences: A380583 A380584 A380585 * A380587 A380588 A380589

Keyword

nonn

Author

Paolo Xausa, Jan 27 2025

Status

approved