A380418 Split A377091 into sublists consisting of runs of terms with the same sign. Then a(n) = 1 if terms (in absolute value) in the n-th sublist form an arithmetic progression with common difference -1, 0 otherwise.

1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0

Offset

1

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

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) ...
And the corresponding terms of the present sequence are therefore:
   1   0      1      0        1      0        0 ...

Mathematica

(* A377091list is defined at A377091 *)
Map[Boole[# == Range[Max[#], Min[#], -1]] &, Abs[Most[SplitBy[A377091list[2000], Sign]]]]

Crossrefs

Cf. A377091, A379882, A380417, A380419, A380422, A380510.

Sequence in context: A273512 A266619 A267587 * A014165 A014141 A014093

Adjacent sequences: A380415 A380416 A380417 * A380419 A380420 A380421

Keyword

nonn

Author

Paolo Xausa, Jan 24 2025

Status

approved