login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=0..74.

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 A056961

Adjacent sequences:  A010878 A010879 A010880 * A010882 A010883 A010884

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 19 02:47 EST 2018. Contains 317332 sequences. (Running on oeis4.)