The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A010873 a(n) = n mod 4. 110
 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Complement of A002265, since 4*A002265(n)+a(n) = n. - Hieronymus Fischer, Jun 01 2007 The rightmost digit in the base-4 representation of n. Also, the equivalent value of the two rightmost digits in the base-2 representation of n. - Hieronymus Fischer, Jun 11 2007 Periodic sequences of this type can be also calculated by a(n) = floor(q/(p^m-1)*p^n) mod p, where q is the number representing the periodic digit pattern and m is the period length. p and q can be calculated as follows: Let D be the array representing the number pattern to be repeated, m = size of D, max = maximum value of elements in D. Than p := max + 1 and q := p^m*sum_{i=1..m} D(i)/p^i. Example: D = (0, 1, 2, 3), p = 4 and q = 57 for this sequence. - Hieronymus Fischer, Jan 04 2013 LINKS Antti Karttunen, Table of n, a(n) for n = 0..65536 Index entries for linear recurrences with constant coefficients, signature (0,0,0,1). FORMULA a(n) = (1/2)*(3-(-1)^n-2*(-1)^floor(n/2)); also a(n) = (1/2)*(3-(-1)^n-2*(-1)^((2n-1+(-1)^n)/4))); also a(n) = (1/2)*(3-(-1)^n-2*sin(Pi/4*(2n+1+(-1)^n))). G.f.: (3x^3+2x^2+x)/(1-x^4). - Hieronymus Fischer, May 29 2007 From Hieronymus Fischer, Jun 11 2007: (Start) Trigonometric representation: a(n)=2^2*(sin(n*Pi/4))^2*sum{1<=k<4, k*product{1<=m<4,m<>k, (sin((n-m)*Pi/4))^2}}. Clearly, the squared terms may be replaced by their absolute values '|.|'. Complex representation: a(n)=1/4*(1-r^n)*sum{1<=k<4, k*product{1<=m<4,m<>k, (1-r^(n-m))}} where r=exp(Pi/2*i)=i=sqrt(-1). All these formulas can be easily adapted to represent any periodic sequence. a(n) = n mod 2+2*(floor(n/2)mod 2) = A000035(n)+2*A000035(A004526(n)). (End) a(n) = 6 - a(n-1) - a(n-2) - a(n-3) for n > 2. - Reinhard Zumkeller, Apr 13 2008 a(n) = 3/2 + cos((n+1)pi)/2 + sqrt(2)cos((2n+3)Pi/4) [Jaume Oliver Lafont, Dec 05 2008] From Hieronymus Fischer, Jan 04 2013: (Start) a(n) = floor(41/3333*10^(n+1)) mod 10. a(n) = floor(19/85*4^(n+1)) mod 4. (End) E.g.f.: 2*sinh(x) - sin(x) + cosh(x) - cos(x). - Stefano Spezia, Apr 20 2021 MAPLE seq(chrem( [n, n], [1, 4] ), n=0..80); # Zerinvary Lajos, Mar 25 2009 MATHEMATICA nn=40; CoefficientList[Series[(x+2x^2+3x^3)/(1-x^4), {x, 0, nn}], x] (* Geoffrey Critzer, Jul 26 2013 *) Table[Mod[n, 4], {n, 0, 100}] (* T. D. Noe, Jul 26 2013 *) PadRight[{}, 120, {0, 1, 2, 3}] (* Harvey P. Dale, Mar 29 2018 *) PROG (PARI) a(n)=n%4 \\ Charles R Greathouse IV, Dec 05 2011 (Haskell) a010873 n = (`mod` 4) a010873_list = cycle [0..3]  -- Reinhard Zumkeller, Jun 05 2012 (Scheme) (define (A010873 n) (modulo n 4)) ;; Antti Karttunen, Nov 07 2017 CROSSREFS Partial sums: A130482. Other related sequences A130481, A130483, A130484, A130485. Cf. A004526, A002264, A002265, A002266. Cf. A000035, A010877. Sequence in context: A319047 A276335 A189480 * A049804 A277904 A132387 Adjacent sequences:  A010870 A010871 A010872 * A010874 A010875 A010876 KEYWORD nonn,easy AUTHOR EXTENSIONS First to third formulas re-edited for better readability by Hieronymus Fischer, Dec 05 2011 Incorrect g.f. removed by Georg Fischer, May 18 2019 STATUS approved

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

Last modified November 26 07:48 EST 2022. Contains 358353 sequences. (Running on oeis4.)