1,2

For this discussion let R(n) (n >= 0) denote A377091(n). Sequence A377091 starts with R(0) = 0. From then on the sequence consists of blocks of consecutive terms all with the same sign. The blocks are defined by eight sequences denoted by Sa, Sb, ..., Sh. The (2k-1)-st block (k >= 1) consists of positive terms running from R(Sa(k)) = Sb(k) to R(Sc(k)) = Sd(k). This is followed by the (2*k)-th block (k >= 1) which consists of negative terms running from R(e(k)) = -Sf(k) to R(g(k)) = -Sh(k).

The sequences Sa, ..., Sh are Sa = A379788, Sb = A379789, Sc = A379790, Sd = A379791, Se = A379792, Sf = A379793, Sg = A380837, and Sh = A379794.

The sequences are related by Sa(k) = Sg(k-1)+1 and Se(k) = Sc(k)+1, and one of each pair could be omitted from the OEIS. However, since the structure of A377091 is already sufficiently confusing, at present all eight sequences have their own entries. This also makes it simpler to define the block lengths, etc., and to use the Plot2 OEIS command.

Paolo Xausa, Table of n, a(n) for n = 1..1000 (terms 1..513 from N. J. A. Sloane).

(* A377091list is defined at A377091 *)

SequencePosition[A377091list[5000], {_?NonPositive, _?Positive}][[All, 1]] (* Paolo Xausa, Feb 05 2025 *)

Cf. A377091, A379789, A379790, A379791, A379792, A379793, A379794, A380837.

Sequence in context: A242644 A002800 A280077 * A372054 A295952 A132174

Adjacent sequences: A379785 A379786 A379787 * A379789 A379790 A379791

N. J. A. Sloane, Jan 17 2025

approved