A062756 Number of 1's in ternary (base-3) expansion of n.
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
Offset: 0
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
Crossrefs
Programs
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Haskell
a062756 0 = 0 a062756 n = a062756 n' + m `mod` 2 where (n',m) = divMod n 3 -- Reinhard Zumkeller, Feb 21 2013
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Mathematica
Table[Count[IntegerDigits[i, 3], 1], {i, 0, 200}] Nest[Join[#, # + 1, #] &, {0}, 5] (* IWABUCHI Yu(u)ki, Sep 08 2012 *) -
PARI
a(n)=if(n<1,0,a(n\3)+(n%3)%2) \\ Paul D. Hanna, Feb 24 2006
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PARI
a(n)=hammingweight(digits(n,3)%2); \\ Ruud H.G. van Tol, Dec 10 2023
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Python
from sympy.ntheory import digits def A062756(n): return digits(n,3)[1:].count(1) # Chai Wah Wu, Dec 23 2022
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
Extensions
More terms from Vladeta Jovovic, Jul 18 2001
Comments