OFFSET
0,10
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
F. T. Adams-Watters, 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.
Wikipedia, Ternary numeral system
FORMULA
a(1)=a(2)=0; a(3n)=a(n)+1; a(3n+1)=a(3n+2)=a(n). a(3^n-2)=a(3^n-1)=0; a(3^n)=n. a(n)=A077266(n, 3).
G.f.: (Sum_{k>=0} x^(3^(k+1))/(1 + x^(3^k) + x^(2*3^k)))/(1-x). - Franklin T. Adams-Watters, Nov 03 2005
EXAMPLE
a(8)=0 since 8 written in base 3 is 22 with 0 zeros;
a(9)=2 since 9 written in base 3 is 100 with 2 zeros;
a(10)=1 since 10 written in base 3 is 101 with 1 zero.
MATHEMATICA
Table[Count[IntegerDigits[n, 3], 0], {n, 0, 6!}] (* Vladimir Joseph Stephan Orlovsky, Jul 25 2009 *)
DigitCount[Range[0, 110], 3, 0] (* Harvey P. Dale, Jul 04 2021 *)
PROG
(Haskell)
a077267 n = a079978 n + if n < 3 then 0 else a077267 (n `div` 3)
-- Reinhard Zumkeller, Feb 21 2013
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Henry Bottomley, Nov 01 2002
EXTENSIONS
a(0)=1 added, offset changed to 0 and b-file adjusted by Reinhard Zumkeller, Feb 21 2013
Wrong formula deleted by Reinhard Zumkeller, Feb 21 2013
STATUS
approved