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Search: id:A010875
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| A010875 |
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Simple periodic sequence. |
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+0
26
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| 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The rightmost digit in the base-6 representation of n. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 11 2007
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FORMULA
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a(n)=n mod 6. Complex representation: a(n)=1/6*(1-r^n)*sum{1<=k<6, k*product{1<=m<6,m<>k, (1-r^(n-m))}} where r=exp(pi/3*i)=(1+sqrt(3)*i)/2 and i=sqrt(-1). Trigonometric representation: a(n)=(16/3)^2*(sin(n*pi/6))^2*sum{1<=k<6, k*product{1<=m<6,m<>k, (sin((n-m)*pi/6))^2}}. G.f.: g(x)=(sum{1<=k<6, k*x^k})/(1-x^6). Also: g(x)=x(5x^6-6x^5+1)/((1-x^6)(1-x)^2). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 31 2007
a(n)=n mod 2+2*(floor(n/2)mod 3)=A000035(n)+2*A010872(A004526(n)). Also: a(n)=n mod 3+3*(floor(n/3)mod 2)=A010872(n)+3*A000035(A002264(n)). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 11 2007
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CROSSREFS
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Partial sums: A130484. Other related sequences A130481, A130482, A130483, A130485.
Sequence in context: A037884 A030567 A049265 this_sequence A095874 A063972 A063973
Adjacent sequences: A010872 A010873 A010874 this_sequence A010876 A010877 A010878
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KEYWORD
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nonn
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AUTHOR
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njas
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