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A081603
Number of 2's in ternary representation of n.
48
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
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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Mar 23 2003
STATUS
approved