A081604 Number of digits in ternary representation of n.

1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset: 0

Author

Reinhard Zumkeller, Mar 23 2003

Keywords

• nonn
• base

Comments

a(n) is the length of row n in table A054635. - Reinhard Zumkeller, Sep 05 2014

Examples

			a(8) = 2 because 8 = 22_3, having 2 digits.
a(9) = 3 because 9 = 100_3, having 3 digits.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Ternary.

Crossrefs

Cf. A003137, A007089, A030341, A049803, A054635, A062153, A070939, A080342.

Cf. A062756, A077267, A081603.

Cf. A134021, A134025, A134026, A246435.

Programs

Haskell

a081604 n = if n < 3 then 1 else a081604 (div n 3) + 1
-- Reinhard Zumkeller, Sep 05 2014, Feb 21 2013

Maple

A081604 := proc(n)
    max(1,1+ilog[3](n)) ;
end proc: # R. J. Mathar, Jul 12 2016

Mathematica

Table[Length[IntegerDigits[n, 3]], {n, 0, 99}] (* Alonso del Arte, Dec 30 2012 *)
Join[{1},IntegerLength[Range[120],3]] (* Harvey P. Dale, Apr 07 2019 *)

Formula

a(n) = A062153(n) + 1 for n >= 1.

a(n) = A077267(n) + A062756(n) + A081603(n);

From Reinhard Zumkeller, Oct 19 2007: (Start)

0 <= A134021(n) - a(n) <= 1;

a(A134025(n)) = A134021(A134025(n));

a(A134026(n)) = A134021(A134026(n)) - 1. (End)

a(n+1) = -Sum_{k=1..n} mu(3*k)*floor(n/k). - Benoit Cloitre, Oct 21 2009

a(n) = floor(log_3(n)) + 1. - Can Atilgan and Murat Erşen Berberler, Dec 05 2012

a(n) = if n < 3 then 1 else a(floor(n/3)) + 1. - Reinhard Zumkeller, Sep 05 2014

G.f.: 1 + (1/(1 - x))*Sum_{k>=0} x^(3^k). - Ilya Gutkovskiy, Jan 08 2017