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A026179 Numbers k such that A026177(j) < A026177(k) for all j < k.

%I A026179 #55 Feb 16 2025 01:11:04
%S A026179 1,2,5,6,8,11,14,15,17,18,20,23,24,26,29,32,33,35,38,41,42,44,45,47,
%T A026179 50,51,53,54,56,59,60,62,65,68,69,71,72,74,77,78,80,83,86,87,89,92,95,
%U A026179 96,98,99,101,104,105,107,110,113,114,116,119
%N A026179 Numbers k such that A026177(j) < A026177(k) for all j < k.
%C A026179 After first term, these are the numbers of the form (3i+2)*3^j, where i >= 0, j >= 0. - _Clark Kimberling_, Oct 19 2016
%C A026179 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]
%C A026179 The asymptotic density of this sequence is 1/2. - _Amiram Eldar_, Apr 03 2022
%H A026179 Amiram Eldar, <a href="/A026179/b026179.txt">Table of n, a(n) for n = 1..10000</a>
%H A026179 F. M. Dekking, <a href="https://arxiv.org/abs/2001.08915">Permutations of N generated by left-right filling algorithms</a>, arXiv:2001.08915 [math.CO], 2020, see R_opos in section 2.3.
%H A026179 Kevin Ryde, <a href="http://user42.tuxfamily.org/terdragon/index.html">Iterations of the Terdragon Curve</a>, see index "TurnRight".
%H A026179 <a href="/index/Ar#3-automatic">Index entries for 3-automatic sequences</a>.
%F A026179 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
%t A026179 a[b_] := Table[Mod[n/b^IntegerExponent[n, b], b], {n, 1, 160}]
%t A026179 p[b_, d_] := Flatten[Position[a[b], d]]
%t A026179 p[3, 1] (* A026225 *)
%t A026179 p[3, 2] (* A026179 without initial 1 *)
%t A026179 (* _Clark Kimberling_, Oct 19 2016 *)
%o A026179 (PARI) a(n) = { if(n>1, n=2*n-2; my(v=digits(n,3));
%o A026179   for(i=1,#v, if(v[i]==1, n++;
%o A026179     forstep(j=#v,i,-1, if(v[j]++>2,v[j]=0,break)))));
%o A026179   n; } \\ _Kevin Ryde_, Apr 23 2021
%o A026179 (Python)
%o A026179 from sympy import integer_log
%o A026179 def A026179(n):
%o A026179     def f(x): return n-1+x-sum(((x//3**i)-2)//3+1 for i in range(integer_log(x,3)[0]+1))
%o A026179     m, k = n, f(n)
%o A026179     while m != k: m, k = k, f(k)
%o A026179     return m # _Chai Wah Wu_, Feb 15 2025
%Y A026179 Cf. A026177, A026180, A026225.
%Y A026179 Cf. A080846 (characteristic function except for 1), A137893.
%K A026179 nonn
%O A026179 1,2
%A A026179 _Clark Kimberling_