This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A010874 a(n) = n mod 5. 50
 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Complement of A002266, since 5*A002266(n) + a(n) = n. - Hieronymus Fischer, Jun 01 2007 LINKS Muniru A Asiru, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1). FORMULA Complex representation: a(n) = (1/5)*(1-r^n)*Sum{1<=k<5, k*Product{1<=m<5,m<>k, (1-r^(n-m))}} where r=exp(2*Pi/5*i) and i=sqrt(-1). G.f.: g(x)=(4*x^4+3*x^3+2*x^2+x)/(1-x^5). - Hieronymus Fischer, May 29 2007 Trigonometric representation: a(n) = (16/5)^2*(sin(n*Pi/5))^2*Sum{1<=k<5, k*Product{1<=m<5,m<>k, (sin((n-m)*Pi/5))^2}}. Clearly, the squared terms may be replaced by their absolute values '|.|'. This formula can be easily adapted to represent any periodic sequence. G.f.: also g(x) = x*(5*x^6 - 6*x^5 + 1)/((1-x^5)*(1-x)^2). - Hieronymus Fischer, Jun 01 2007 a(n) = -cos(4/5*Pi*n)-cos(2/5*Pi*n)+1/20*5^(1/2)*(10-2*5^(1/2))^(1/2)* sin(4/5*Pi*n)-1/4*(10-2*5^(1/2))^(1/2)*sin(4/5*Pi*n)-1/4*(10+2*5^(1/2))^(1/2)*sin(2/5*Pi*n)-1/20*5^(1/2)*(10+2*5^(1/2))^(1/2)*sin(2/5*Pi*n) + 2. - Leonid Bedratyuk, May 14 2012 a(n) = floor(1234/99999*10^(n+1)) mod 10. - Hieronymus Fischer, Jan 03 2013 a(n) = floor(97/1562*5^(n+1)) mod 5. - Hieronymus Fischer, Jan 04 2013 From Wesley Ivan Hurt, Jul 23 2016: (Start) a(n) = a(n-5) for n>4. a(n) = 4*(1 - floor(n/5)) + Sum_{k=1..4} floor((n-k)/5). a(n) = 4 - 4*floor(n/5) + floor((n-1)/5) + floor((n-2)/5) + floor((n-3)/5) + floor((n-4)/5). a(n) = n - 5*floor(n/5). (End) a(n) = 2 + (2/5)*Sum_{k=1..4} k*((cos(2*(n-k)*Pi/5) + cos(4*(n-k)*Pi/5)). - Wesley Ivan Hurt, Sep 27 2018 MAPLE seq(chrem( [n, n], [1, 5] ), n=0..80); # Zerinvary Lajos, Mar 25 2009 MATHEMATICA Mod[Range[0, 100], 5] (* Wesley Ivan Hurt, Jul 23 2016 *) PROG (PARI) a(n)=n%5 \\ Charles R Greathouse IV, Sep 24 2015 (MAGMA) [n mod 5 : n in [0..100]]; // Wesley Ivan Hurt, Jul 23 2016 (GAP) List([0..100], n->n mod 5); # Muniru A Asiru, Sep 28 2018 CROSSREFS Partial sums: A130483. Cf. A130481, A130482, A130484, A130485, A004526, A002264, A002265, A002266. Sequence in context: A031235 A090141 A049264 * A278182 A309956 A125926 Adjacent sequences:  A010871 A010872 A010873 * A010875 A010876 A010877 KEYWORD nonn,easy AUTHOR 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 16 10:36 EDT 2019. Contains 327094 sequences. (Running on oeis4.)