This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A010874 a(n) = n mod 5. 45
 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 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) 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 CROSSREFS Partial sums: A130483. Cf. A130481, A130482, A130484, A130485, A004526, A002264, A002265, A002266. Sequence in context: A031235 A090141 A049264 * A278182 A125926 A125923 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.