A380503 - OEIS

A380503

Split A377091 into sublists consisting of runs of terms with the same sign. Sequence gives k's such that A377091(k) is the first term of those sublists whose terms (in absolute value) form an arithmetic progression with common difference 1.

0, 1, 5, 10, 26, 37, 53, 82, 101, 122, 148, 197, 226, 257, 290, 325, 401, 442, 485, 530, 1093, 1157, 1370, 1526, 1602, 1682, 1765, 1850, 2116, 2210, 2306, 2403, 2501, 2602, 2708, 2920, 3026, 3137, 3365, 3482, 3601, 3722, 3970, 4097, 4226, 4357, 4493, 4762, 4901, 5042

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

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:

0 1 * 5 * 10 * ...

(where * indicates sublists whose terms do not form an arithmetic progression with common difference 1).

LINKS

Table of n, a(n) for n=1..50.

MATHEMATICA

(* A377091list is defined at A377091 *)

With[{A377091 = A377091list[10000]}, Flatten[Map[FirstPosition[A377091, First[#]] - 1 &, Select[Most[SplitBy[A377091, Sign]], Abs[#] == Range[Min[Abs[#]], Max[Abs[#]]] &]]]]

CROSSREFS

Cf. A377091, A379882, A380417, A380420, A380504, A380505.

Sequence in context: A083010 A324005 A166388 * A290055 A066872 A301537

Adjacent sequences: A380500 A380501 A380502 * A380504 A380505 A380506

KEYWORD

nonn

AUTHOR

Paolo Xausa, Jan 25 2025

STATUS

approved