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.
MATHEMATICA
Mod[Range[0, 100], 12] (* Paolo Xausa, Feb 02 2024 *)
PROG
(PARI) A010881(n)=n%12 \\ M. F. Hasler, Sep 25 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved