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
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.
Michael Gilleland, Some Self-Similar Integer Sequences
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".
Robert Walker, Self Similar Sloth Canon Number Sequences
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
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