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A062756 Number of 1's in ternary (base-3) expansion of n. 55
0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 4, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 4, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Fixed point of the morphism: 0 ->010; 1 ->121; 2 ->232; ...; n -> n(n+1)n, starting from a(0)=0. - Philippe Deléham, Oct 25 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.
S. Northshield, An Analogue of Stern's Sequence for Z[sqrt(2)], Journal of Integer Sequences, 18 (2015), #15.11.6.
Kevin Ryde, Iterations of the Terdragon Curve, see index "dir".
FORMULA
a(0) = 0, a(3n) = a(n), a(3n+1) = a(n)+1, a(3n+2) = a(n). - Vladeta Jovovic, Jul 18 2001
G.f.: (Sum_{k>=0} x^(3^k)/(1+x^(3^k)+x^(2*3^k)))/(1-x). In general, the generating function for the number of digits equal to d in the base b representation of n (0 < d < b) is (Sum_{k>=0} x^(d*b^k)/(Sum_{i=0..b-1} x^(i*b^k)))/(1-x). - Franklin T. Adams-Watters, Nov 03 2005 [For d=0, use the above formula with d=b: (Sum_{k>=0} x^(b^(k+1))/(Sum_{i=0..b-1} x^(i*b^k)))/(1-x), adding 1 if you consider the representation of 0 to have one zero digit.]
a(n) = a(floor(n/3)) + (n mod 3) mod 2. - Paul D. Hanna, Feb 24 2006
MATHEMATICA
Table[Count[IntegerDigits[i, 3], 1], {i, 0, 200}]
Nest[Join[#, # + 1, #] &, {0}, 5] (* IWABUCHI Yu(u)ki, Sep 08 2012 *)
PROG
(PARI) a(n)=if(n<1, 0, a(n\3)+(n%3)%2) \\ Paul D. Hanna, Feb 24 2006
(PARI) a(n)=hammingweight(digits(n, 3)%2); \\ Ruud H.G. van Tol, Dec 10 2023
(Haskell)
a062756 0 = 0
a062756 n = a062756 n' + m `mod` 2 where (n', m) = divMod n 3
-- Reinhard Zumkeller, Feb 21 2013
(Python)
from sympy.ntheory import digits
def A062756(n): return digits(n, 3)[1:].count(1) # Chai Wah Wu, Dec 23 2022
CROSSREFS
Cf. A080846, A343785 (first differences).
Cf. A081606 (indices of !=0).
Indices of terms 0..6: A005823, A023692, A023693, A023694, A023695, A023696, A023697.
Numbers of: A077267 (0's), A081603 (2's), A160384 (1's+2's).
Other bases: A000120, A160381, A268643.
Sequence in context: A030372 A065363 A119995 * A360676 A334107 A346700
KEYWORD
nonn,base
AUTHOR
Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 16 2001
EXTENSIONS
More terms from Vladeta Jovovic, Jul 18 2001
STATUS
approved

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Last modified March 18 22:34 EDT 2024. Contains 370951 sequences. (Running on oeis4.)