This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A010875 a(n) = n mod 6. 44
 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Period 6: repeat [0, 1, 2, 3, 4, 5]. The rightmost digit in the base-6 representation of n. - Hieronymus Fischer, Jun 11 2007 [a(n) * a(m)] mod 6 == a(n*m mod 6) == a(n*m). - Jon Perry, Nov 11 2014 If n > 3 and (a(n) is in {0,2,3,4}), then n is not prime. - Jean-Marc Rebert, Jul 22 2015, corrected by M. F. Hasler, Jul 24 2015 LINKS Antti Karttunen, Table of n, a(n) for n = 0..65538 Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1). FORMULA Complex representation: a(n) = (1/6)*(1-r^n)*sum{1<=k<6, k * product{1<=m<6,m<>k, (1-r^(n-m))}}, where r=exp(Pi/3*i)=(1+sqrt(3)*i)/2 and i=sqrt(-1). Trigonometric representation: a(n) = (16/3)^2*(sin(n*Pi/6))^2*sum{1<=k<6, k*product{1<=m<6,m<>k, (sin((n-m)*Pi/6))^2}}. G.f.: g(x) = (sum{1<=k<6, k*x^k})/(1-x^6). Also: g(x) = x(5x^6-6x^5+1)/((1-x^6)(1-x)^2). - Hieronymus Fischer, May 31 2007 a(n) = (n mod 2) + 2(floor(n/2) mod 3) = A000035(n) +2*A010872(A004526(n)); a(n) = (n mod 3) + 3(floor(n/3) mod 2) = A010872(n) +3*A000035(A002264(n)). - Hieronymus Fischer, Jun 11 2007 a(n) = 2.5-0.5*(-1)^n-cos(Pi*n/3)-3^0.5*sin(Pi*n/3)-cos(2*Pi*n/3)-3^0.5/3*sin(2*Pi*n/3). - Richard Choulet, Dec 11 2008 a(n) = n^3 mod 6. - Zerinvary Lajos, Oct 29 2009 a(n) = floor(12345/999999*10^(n+1)) mod 10. - Hieronymus Fischer, Jan 03 2013 a(n) = floor(373/9331*6^(n+1)) mod 6. - Hieronymus Fischer, Jan 04 2013 a(n) = 5/2-(-1)^n/2-2*0^((-1)^(n/6-1/12+(-1)^n/12)-(-1)^(n/2-1/4+(-1)^n/4))+2*0^((-1)^(n/6+1/4+(-1)^n/12)+(-1)^(n/2-1/4+(-1)^n/4)). - Wesley Ivan Hurt, Jun 23 2015 E.g.f.: -sqrt(3)*exp(x/2)*sin(sqrt(3)*x/2) - 2*cosh(x/2)*cos(sqrt(3)*x/2). - Robert Israel, Jul 22 2015 MAPLE A010875:=n->n mod 6; seq(A010875(n), n=0..100); # Wesley Ivan Hurt, Jul 06 2014 MATHEMATICA Mod[Range[0, 100], 6] (* Wesley Ivan Hurt, Jul 06 2014 *) PROG (Sage) [power_mod(n, 3, 6 )for n in xrange(0, 81)] # Zerinvary Lajos, Oct 29 2009 (PARI) a(n)=n%6 \\ Charles R Greathouse IV, Dec 05 2011 (MAGMA) [n mod 6: n in [0..100]]; // Wesley Ivan Hurt, Jul 06 2014 (Scheme) (define (A010875 n) (modulo n 6)) ;; Antti Karttunen, Dec 22 2017 CROSSREFS Partial sums: A130484. Other related sequences A130481, A130482, A130483, A130485. Cf. also A079979, A097325, A122841. Sequence in context: A303534 A030567 A049265 * A260187 A257687 A220660 Adjacent sequences:  A010872 A010873 A010874 * A010876 A010877 A010878 KEYWORD nonn,easy AUTHOR EXTENSIONS Formulas 1 to 6 re-edited for better readability by Hieronymus Fischer, Dec 05 2011 More terms from Antti Karttunen, Dec 22 2017 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.

Last modified October 15 05:56 EDT 2018. Contains 316202 sequences. (Running on oeis4.)