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

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, 31, 36, 37, 39, 40, 41, 43, 44, 49, 50, 52, 53, 54, 56, 60, 62, 67, 68, 70, 71, 72, 74, 76, 77, 78, 79, 80, 81, 82, 84, 85, 90, 91, 93, 94, 108, 109, 111, 112, 117, 118, 120, 121, 122

Offset: 1

Author

Reinhard Zumkeller, Jan 07 2009

Keywords

• base
• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Robert Baillie and Thomas Schmelzer, Summing Kempner's Curious (Slowly-Convergent) Series, Mathematica Notebook kempnerSums.nb, Wolfram Library Archive, 2008.

Crossrefs

Complement of A031944.

Union of A032924, A005823 and A005836.

Cf. A007089, A043530, A212193.

Programs

Haskell

import Data.List (findIndices)
a154314 n = a154314_list !! (n-1)
a154314_list = findIndices (/= 3) a212193_list
-- Reinhard Zumkeller, May 04 2012

Mathematica

Select[Range[0,200],Length[Union[IntegerDigits[#,3]]]<3&] (* Harvey P. Dale, Nov 23 2012 *)

PARI

is(n)=#Set(digits(n,3))<3 \\ Charles R Greathouse IV, Mar 17 2014

Formula

A043530(a(n)) <= 2.

A212193(a(n)) <> 3. - Reinhard Zumkeller, May 04 2012

a(n) >> n^1.58..., where the exponent is log(3)/log(2). - Charles R Greathouse IV, Mar 17 2014

Sum_{n>=2} 1/a(n) = 5.47555542241781419692840472181029603722178623821762258873485212626135391726959422416350447132335696748507... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - Amiram Eldar, Apr 14 2025