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 A010881 Simple periodic sequence: n mod 12. 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, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The value of the rightmost digit in the base-12 representation of n. - Hieronymus Fischer, Jun 11 2007 LINKS Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,1). FORMULA 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, 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, Jun 11 2007 a(A001248(k) + 17) = 6 for k>2. - Reinhard Zumkeller, May 12 2010 a(n) = A034326(n+1)-1. - M. F. Hasler, Sep 25 2014 EXAMPLE a(27)=3 since 27=12*2+3. PROG (PARI) A010881(n)=n%12 \\ M. F. Hasler, Sep 25 2014 CROSSREFS Partial sums: A130490. Other related sequences A130481, A130482, A130483, A130484, A130485, A130486, A130487, A130488, A130489. Sequence in context: A130024 A131232 A297238 * A190600 A053832 A345672 Adjacent sequences:  A010878 A010879 A010880 * A010882 A010883 A010884 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified June 29 18:25 EDT 2022. Contains 354913 sequences. (Running on oeis4.)