A380504 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, 3, 8, 1024, 1088, 1225, 1521, 1599, 2303, 2400, 2915, 8648, 8835, 9801, 10404, 12543, 12996, 13456, 14400, 14641, 15376, 17688, 17955, 19321, 20736, 40804, 47961, 54289, 55695, 56644, 58081, 60025, 60516, 64516, 65025, 66049, 66564, 71823, 72360, 75076, 77841

Offset

1,2

Links

Table of n, a(n) for n=1..41.

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:
   0   *      3      *        8      *        * ...
(where * indicates sublists whose terms do not form an arithmetic progression with common difference -1).

Mathematica

(* A377091list is defined at A377091 *)
With[{A377091 = A377091list[20000]}, Flatten[Map[FirstPosition[A377091, First[#]] - 1 &, Select[Most[SplitBy[A377091, Sign]], Abs[#] == Range[Max[Abs[#]], Min[Abs[#]], -1] &]]]]

Crossrefs

Cf. A377091, A379882, A380418, A380422, A380503, A380505.

Sequence in context: A297527 A268141 A354119 * A278974 A063103 A058847

Adjacent sequences: A380501 A380502 A380503 * A380505 A380506 A380507

Keyword

nonn

Author

Paolo Xausa, Jan 26 2025

Status

approved