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A062756 Number of 1's in ternary (base-3) expansion of n. 38
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

R. 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

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.

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).

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

(Haskell)

a062756 0 = 0

a062756 n = a062756 n' + m `mod` 2 where (n', m) = divMod n 3

-- Reinhard Zumkeller, Feb 21 2013

CROSSREFS

Cf. A005823, A023693, A023694, A023695, A023696, A023697, A032924, A043321, A023692, A000120, A077267.

Cf. A080846, A081603.

Sequence in context: A030372 A065363 A119995 * A334107 A301574 A272728

Adjacent sequences:  A062753 A062754 A062755 * A062757 A062758 A062759

KEYWORD

nonn,base

AUTHOR

Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 16 2001

EXTENSIONS

Formula and more terms from Vladeta Jovovic, Jul 18 2001

STATUS

approved

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Last modified May 27 18:56 EDT 2020. Contains 334664 sequences. (Running on oeis4.)