A132141 Numbers whose ternary representation begins with 1.

1, 3, 4, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108

Offset

1,2

Comments

The lower and upper asymptotic densities of this sequence are 1/2 and 3/4, respectively. - Amiram Eldar, Feb 28 2021

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Bryan Brown, Michael Dairyko, Stephan Ramon Garcia, Bob Lutz and Michael Someck, Four quotient set gems, The American Mathematical Monthly, Vol. 121, No. 7 (2014), pp. 590-598; arXiv preprint, arXiv:1312.1036 [math.NT], 2013.

Christian Mauduit, Propriétés arithmétiques des substitutions, in Séminaire de Théorie des Nombres, Paris, 1989-90, pp. 177-190 (in French).

Index entries for 3-automatic sequences.

Formula

A number n is a term iff 3^m <= n < 2*3^m -1, for m=0,1,2,... - Zak Seidov, Mar 03 2009

a(n) = n + (3^floor(log_3(2*n)) - 1)/2. - Kevin Ryde, Feb 19 2022

Mathematica

Flatten[(Range[3^#, 2 3^#-1])&/@Range[0, 4]] (* Zak Seidov, Mar 03 2009 *)

Prog

(PARI) s=[]; for(n=0, 4, for(x=3^n, 2*3^n-1, s=concat(s, x))); s \\ Zak Seidov, Mar 03 2009
(PARI) a(n) = n + 3^logint(n<<1, 3) >> 1; \\ Kevin Ryde, Feb 19 2022
(Haskell)
a132141 n = a132141_list !! (n-1)
a132141_list = filter ((== 1) . until (< 3) (flip div 3)) [1..]
-- Reinhard Zumkeller, Feb 06 2015

Crossrefs

Cf. A007089, A132140, A157671, A131835.

Sequence in context: A098801 A259615 A069807 * A246303 A362461 A285161

Adjacent sequences: A132138 A132139 A132140 * A132142 A132143 A132144

Keyword

nonn,base,easy

Author

Reinhard Zumkeller, Aug 20 2007

Status

approved