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Search: id:A010881
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| A010881 |
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Simple periodic sequence: n mod 12. |
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+0
5
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| 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 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 value of the rightmost digit in the base-12 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 12. Complex representation: a(n)=1/12*(1-r^n)*sum{1<=k<12, k*product{1<=m<12,m<>k, (1-r^(n-m))}} where r=exp(pi/6*i)=(sqrt(3)+i)/2 and i=sqrt(-1). Trigonometric representation: a(n)=(512/3)^2*(sin(n*pi/12))^2*sum{1<=k<12, k*product{1<=m<12,m<>k, (sin((n-m)*pi/12))^2}}. G.f.: g(x)=(sum{1<=k<12, k*x^k})/(1-x^12). Also: g(x)=x(11x^12-12x^11+1)/((1-x^12)(1-x)^2). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 31 2007
a(n)=n mod 2+2*(floor(n/2)mod 6)=A000035(n)+2*A010875(A004526(n)). Also: a(n)=n mod 3+3*(floor(n/3)mod 4)=A010872(n)+3*A010873(A002264(n)). Also: a(n)=n mod 4+4*(floor(n/4)mod 3)=A010873(n)+4*A010872(A002265(n)). Also: a(n)=n mod 6+6*(floor(n/6)mod 2)=A010875(n)+6*A000035(floor(n/6)). Also: a(n)=n mod 2+2*(floor(n/2)mod 2+4*(floor(n/4)mod 3)=A000035(n)+2*A000035(A004526(n))+4*A010872(A002265(n)). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 11 2007
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EXAMPLE
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a(27)=3 since 27=12*2+3
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CROSSREFS
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Partial sums: A130490. Other related sequences A130481, A130482, A130483, A130484, A130485, A130486, A130487, A130488, A130489.
Adjacent sequences: A010878 A010879 A010880 this_sequence A010882 A010883 A010884
Sequence in context: A017895 A130024 A131232 this_sequence A053832 A056961 A043271
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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