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A081603
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Number of 2's in ternary representation of n.
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34
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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
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OFFSET
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0,9
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COMMENTS
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Fixed point of the morphism: 0 ->001; 1 ->112; 2 ->223; 3 ->334, etc., starting from a(0)=0. - Philippe Deléham, Oct 26 2011
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LINKS
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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.
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FORMULA
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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.
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(Haskell)
a081603 0 = 0
a081603 n = a081603 n' + m `div` 2 where (n', m) = divMod n 3
-- Reinhard Zumkeller, Feb 21 2013
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CROSSREFS
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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
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KEYWORD
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nonn,base
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AUTHOR
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Reinhard Zumkeller, Mar 23 2003
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STATUS
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approved
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