A380510 Split A377091 into sublists consisting of runs of terms with the same sign. Then a(n) = 1 if sorted terms in the n-th sublist form an arithmetic progression with common difference 1, 0 otherwise.

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

Offset

1

Links

Paolo Xausa, Table of n, a(n) for n = 1..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) (13, 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) (9, 10, 11, 12, 13) ...
And the corresponding terms of the present sequence are therefore:
   1   1      1      1        1      1         1                          1 ...

Mathematica

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

Crossrefs

Cf. A377091, A379882, A380417, A380418, A380419.

Sequence in context: A015772 A016288 A016030 * A123271 A121238 A186032

Adjacent sequences: A380507 A380508 A380509 * A380511 A380512 A380513

Keyword

nonn

Author

Paolo Xausa, Jan 26 2025

Status

approved