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A062756
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Number of 1's in ternary (base 3) expansion of n.
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22
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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; internal format)
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OFFSET
| 0,5
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COMMENTS
| Fixed point of the morphism : 0 ->010 ; 1 ->121 ; 2 ->232 ; ... ; n ->n(n+1)n , starting from a(0)=0. - From DELEHAM Philippe, Oct 25 2011.
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 0..10000
Michael Gilleland, Some Self-Similar Integer Sequences
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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_{0<=i<b} 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_{0<=i<b} 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 (pauldhanna(AT)juno.com), Feb 24 2006
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MATHEMATICA
| Table[Count[IntegerDigits[i, 3], 1], {i, 0, 200}]
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PROG
| (PARI) a(n)=if(n<1, 0, a(n\3)+(n%3)%2) - Paul D. Hanna (pauldhanna(AT)juno.com), Feb 24 2006
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CROSSREFS
| Cf. A005823, A023693-A023697, A032924, A043321, A023692, A000120, A077267.
Cf. A080846, A081603.
Sequence in context: A030372 A065363 A119995 * A174695 A165577 A116422
Adjacent sequences: A062753 A062754 A062755 * A062757 A062758 A062759
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KEYWORD
| nonn,base,changed
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AUTHOR
| Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 16 2001
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EXTENSIONS
| Formula and more terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 18 2001
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