A026179 - OEIS

A026179

Numbers k such that A026177(j) < A026177(k) for all j < k.

1, 2, 5, 6, 8, 11, 14, 15, 17, 18, 20, 23, 24, 26, 29, 32, 33, 35, 38, 41, 42, 44, 45, 47, 50, 51, 53, 54, 56, 59, 60, 62, 65, 68, 69, 71, 72, 74, 77, 78, 80, 83, 86, 87, 89, 92, 95, 96, 98, 99, 101, 104, 105, 107, 110, 113, 114, 116, 119

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

OFFSET

1,2

COMMENTS

After first term, these are the numbers of the form (3i+2)*3^j, where i >= 0, j >= 0. - Clark Kimberling, Oct 19 2016

Old conjecture: (a(n)) = complement of A026225 after removal of the initial 1 here. [Note that following the proof of the form of its terms, A026225 has been renamed accordingly. - Peter Munn, Mar 24 2022]

The asymptotic density of this sequence is 1/2. - Amiram Eldar, Apr 03 2022

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

F. M. Dekking, Permutations of N generated by left-right filling algorithms, arXiv:2001.08915 [math.CO], 2020, see R_opos in section 2.3.

Kevin Ryde, Iterations of the Terdragon Curve, see index "TurnRight".

Index entries for 3-automatic sequences.

FORMULA

Let the sequence 1, 0, 1, 1, 0, 0, 1, 0, 1, ... (A137893) be defined as the fixed point of the morphism 1->101 and 0->100, starting from a(1)=1. The indices of 0 are 2, 5, 6, 8, 11, 14, 17, 18, ... (this sequence with first term omitted). - Philippe Deléham, Jun 27 2006

MATHEMATICA

a[b_] := Table[Mod[n/b^IntegerExponent[n, b], b], {n, 1, 160}]

p[b_, d_] := Flatten[Position[a[b], d]]

p[3, 1] (* A026225 *)

p[3, 2] (* A026179 without initial 1 *)

(* Clark Kimberling, Oct 19 2016 *)

PROG

(PARI) a(n) = { if(n>1, n=2*n-2; my(v=digits(n, 3));

for(i=1, #v, if(v[i]==1, n++;

forstep(j=#v, i, -1, if(v[j]++>2, v[j]=0, break)))));

n; } \\ Kevin Ryde, Apr 23 2021

CROSSREFS