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A154314 Numbers with not more than two distinct digits in ternary representation.

%I A154314 #17 Apr 14 2025 05:33:07
%S A154314 0,1,2,3,4,5,6,7,8,9,10,12,13,14,16,17,18,20,22,23,24,25,26,27,28,30,
%T A154314 31,36,37,39,40,41,43,44,49,50,52,53,54,56,60,62,67,68,70,71,72,74,76,
%U A154314 77,78,79,80,81,82,84,85,90,91,93,94,108,109,111,112,117,118,120,121,122
%N A154314 Numbers with not more than two distinct digits in ternary representation.
%H A154314 Reinhard Zumkeller, <a href="/A154314/b154314.txt">Table of n, a(n) for n = 1..10000</a>
%H A154314 Robert Baillie and Thomas Schmelzer, <a href="https://library.wolfram.com/infocenter/MathSource/7166/">Summing Kempner's Curious (Slowly-Convergent) Series</a>, Mathematica Notebook kempnerSums.nb, Wolfram Library Archive, 2008.
%F A154314 A043530(a(n)) <= 2.
%F A154314 A212193(a(n)) <> 3. - _Reinhard Zumkeller_, May 04 2012
%F A154314 a(n) >> n^1.58..., where the exponent is log(3)/log(2). - _Charles R Greathouse IV_, Mar 17 2014
%F A154314 Sum_{n>=2} 1/a(n) = 5.47555542241781419692840472181029603722178623821762258873485212626135391726959422416350447132335696748507... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - _Amiram Eldar_, Apr 14 2025
%t A154314 Select[Range[0,200],Length[Union[IntegerDigits[#,3]]]<3&] (* _Harvey P. Dale_, Nov 23 2012 *)
%o A154314 (Haskell)
%o A154314 import Data.List (findIndices)
%o A154314 a154314 n = a154314_list !! (n-1)
%o A154314 a154314_list = findIndices (/= 3) a212193_list
%o A154314 -- _Reinhard Zumkeller_, May 04 2012
%o A154314 (PARI) is(n)=#Set(digits(n,3))<3 \\ _Charles R Greathouse IV_, Mar 17 2014
%Y A154314 Complement of A031944.
%Y A154314 Union of A032924, A005823 and A005836.
%Y A154314 Cf. A007089, A043530, A212193.
%K A154314 base,nonn
%O A154314 1,3
%A A154314 _Reinhard Zumkeller_, Jan 07 2009