This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A010881 #32 Jul 08 2025 01:47:27
%S A010881 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,
%T A010881 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,
%U A010881 3,4,5,6,7,8,9,10,11,0,1,2,3,4,5,6,7,8,9,10,11
%N A010881 Simple periodic sequence: n mod 12.
%C A010881 The value of the rightmost digit in the base-12 representation of n. - _Hieronymus Fischer_, Jun 11 2007
%H A010881 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,1).
%F A010881 From _Hieronymus Fischer_, May 31 2007: (Start)
%F A010881 a(n) = n mod 12.
%F A010881 Complex representation: a(n) = (1/12)*(1-r^n)*Sum_{k=1..11} k*Product_{m=1..11, m<>k} (1-r^(n-m)) where r = exp(Pi/6*i) = (sqrt(3)+i)/2 and i = sqrt(-1).
%F A010881 Trigonometric representation: a(n) = (512/3)^2*(sin(n*Pi/12))^2*Sum_{k=1..11} k*Product_{m=1..11, m<>k} (sin((n-m)*Pi/12))^2.
%F A010881 G.f.: (Sum_{k=1..11} k*x^k)/(1-x^12).
%F A010881 G.f.: x*(11*x^12-12*x^11+1)/((1-x^12)*(1-x)^2). (End)
%F A010881 From _Hieronymus Fischer_, Jun 11 2007: (Start)
%F A010881 a(n) = (n mod 2)+2*(floor(n/2) mod 6) = A000035(n)+2*A010875(A004526(n)).
%F A010881 a(n) = (n mod 3)+3*(floor(n/3) mod 4) = A010872(n)+3*A010873(A002264(n)).
%F A010881 a(n) = (n mod 4)+4*(floor(n/4) mod 3) = A010873(n)+4*A010872(A002265(n)).
%F A010881 a(n) = (n mod 6)+6*(floor(n/6) mod 2) = A010875(n)+6*A000035(A152467(n)).
%F A010881 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)). (End)
%F A010881 a(A001248(k) + 17) = 6 for k>2. - _Reinhard Zumkeller_, May 12 2010
%F A010881 a(n) = A034326(n+1)-1. - _M. F. Hasler_, Sep 25 2014
%e A010881 a(27) = 3 since 27 = 12*2+3.
%t A010881 Mod[Range[0, 100], 12] (* _Paolo Xausa_, Feb 02 2024 *)
%o A010881 (PARI) A010881(n)=n%12 \\ _M. F. Hasler_, Sep 25 2014
%Y A010881 Partial sums: A130490. Other related sequences A130481, A130482, A130483, A130484, A130485, A130486, A130487, A130488, A130489.
%K A010881 nonn,easy
%O A010881 0,3
%A A010881 _N. J. A. Sloane_