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A010878
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a(n) = n mod 9.
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32
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0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5
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OFFSET
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0,3
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COMMENTS
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Periodic with period of length 9. The digital root of n (A010888) is a very similar sequence.
The rightmost digit in the base-9 representation of n. Also, the equivalent value of the two rightmost digits in the base-3 representation of n. - Hieronymus Fischer, Jun 11 2007
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LINKS
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Ely Golden, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1).
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FORMULA
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Complex representation: a(n)=(1/9)*(1-r^n)*sum{1<=k<9, k*product{1<=m<9,m<>k, (1-r^(n-m))}} where r=exp(2*pi/9*i) and i=sqrt(-1). Trigonometric representation: a(n)=(256/9)^2*(sin(n*pi/9))^2*sum{1<=k<9, k*product{1<=m<9,m<>k, (sin((n-m)*pi/9))^2}}. G.f.: g(x)=(sum{1<=k<9, k*x^k})/(1-x^9). Also: g(x)=x(8x^9-9x^8+1)/((1-x^9)(1-x)^2). - Hieronymus Fischer, May 31 2007
a(n) = n mod 3 + 3*(floor(n/3)mod 3) = A010872(n) + 3*A010872(A002264(n)). - Hieronymus Fischer, Jun 11 2007
a(n) = floor(12345678/999999999*10^(n+1)) mod 10. - Hieronymus Fischer, Jan 03 2013
a(n) = floor(1513361/96855122*9^(n+1)) mod 9. - Hieronymus Fischer, Jan 04 2013
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MAPLE
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A010878 := proc(n)
modp(n, 9) ;
end proc:
seq(A010878(n), n=0..100) ; # R. J. Mathar, Sep 09 2015
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MATHEMATICA
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Array[Mod[#, 9]&, 105, 0] (* Jean-François Alcover, Jan 30 2018 *)
PadRight[{}, 120, Range[0, 8]] (* Harvey P. Dale, Dec 19 2018 *)
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PROG
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(Haskell)
a010878 = (`mod` 9)
a010878_list = cycle [0..8] -- Reinhard Zumkeller, Jan 09 2013
(PARI) a(n)=n%9 \\ Charles R Greathouse IV, Sep 24 2015
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CROSSREFS
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Partial sums: A130487. Other related sequences A130481, A130482, A130483, A130484, A130485, A130486.
Sequence in context: A207505 A235049 A031087 * A309788 A326746 A257849
Adjacent sequences: A010875 A010876 A010877 * A010879 A010880 A010881
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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