A081603 Number of 2's in ternary representation of n.

0, 0, 1, 0, 0, 1, 1, 1, 2, 0, 0, 1, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 3, 0, 0, 1, 0, 0, 1, 1, 1, 2, 0, 0, 1, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 3, 3, 4, 0, 0, 1, 0, 0, 1, 1, 1, 2, 0, 0, 1, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2

Offset

0,9

Comments

Fixed point of the morphism: 0 ->001; 1 ->112; 2 ->223; 3 ->334, etc., starting from a(0)=0. - Philippe Deléham, Oct 26 2011

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

F. T. Adams-Watters and F. Ruskey, Generating Functions for the Digital Sum and Other Digit Counting Sequences, JIS 12 (2009) 09.5.6.

Eric Weisstein's World of Mathematics, Ternary.

Formula

a(n) = floor(n/2) if n < 3, otherwise a(floor(n/3)) + floor((n mod 3)/2).

A077267(n) + A062756(n) + a(n) = A081604(n);

a(n) = (A053735(n) - A062756(n))/2.

Maple

A081603 := proc(n)
    local a, d ;
    a := 0 ;
    for d in convert(n, base, 3) do
        if d= 2 then
            a := a+1 ;
        end if;
    end do:
    a;
end proc: # R. J. Mathar, Jul 12 2016

Mathematica

Table[Count[IntegerDigits[n, 3], 2], {n, 0, 6!}] (* Vladimir Joseph Stephan Orlovsky, Jul 25 2009 *)
Nest[ Flatten[# /. a_Integer -> {a, a, a + 1}] &, {0}, 5] (* Robert G. Wilson v, May 20 2014 *)
DigitCount[Range[0, 120], 3, 2] (* Harvey P. Dale, Jul 10 2019 *)

Prog

(Haskell)
a081603 0 = 0
a081603 n = a081603 n' + m `div` 2 where (n', m) = divMod n 3
-- Reinhard Zumkeller, Feb 21 2013
(PARI) a(n)=hammingweight(digits(n, 3)\2); \\ Ruud H.G. van Tol, Dec 10 2023
(Python)
from gmpy2 import digits
def A081603(n): return digits(n, 3).count('2') # Chai Wah Wu, Dec 05 2024

Crossrefs

Cf. A007089, A074940, A005836, A081610, A081611, A117592 (2^a(n)).

Sequence in context: A091970 A093955 A330168 * A273513 A330005 A165277

Adjacent sequences: A081600 A081601 A081602 * A081604 A081605 A081606

Keyword

nonn,base

Author

Reinhard Zumkeller, Mar 23 2003

Status

approved