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

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

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.

Crossrefs

Cf. A026177, A026180, A026225.

Cf. A080846 (characteristic function except for 1), A137893.

Programs

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 *)

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

Python

from sympy import integer_log
def A026179(n):
    def f(x): return n-1+x-sum(((x//3**i)-2)//3+1 for i in range(integer_log(x,3)[0]+1))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Feb 15 2025

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