A379788 Sequence Sa of the eight sequences defining the blocks of terms in A377091.

1, 5, 10, 21, 32, 43, 61, 82, 101, 122, 148, 184, 211, 242, 273, 308, 343, 401, 442, 485, 530, 577, 652, 704, 758, 814, 872, 932, 966, 1024, 1060, 1090, 1126, 1191, 1229, 1297, 1370, 1409, 1449, 1521, 1526, 1599, 1604, 1682, 1765, 1850, 1937, 2071, 2118, 2210, 2303, 2308, 2400, 2405, 2501, 2602, 2708, 2863, 2917, 2973

Offset: 1

Author

N. J. A. Sloane, Jan 17 2025

Keywords

• nonn

Comments

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.

Links

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

Crossrefs

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

Programs

Mathematica

(* A377091list is defined at A377091 *)
SequencePosition[A377091list[5000], {?NonPositive, ?Positive}][[All, 1]] (* Paolo Xausa, Feb 05 2025 *)