A010883 Simple periodic sequence: repeat 1,2,3,4.

1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Partial sums are given by A130482(n) + n + 1. - Hieronymus Fischer, Jun 08 2007

1234/9999 = 0.123412341234... - Eric Desbiaux, Nov 03 2008

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).

Crossrefs

Cf. A010872, A010873, A010874, A010875, A010876, A004526, A002264, A002265, A002266.

Cf. A177037 (decimal expansion of (9+2*sqrt(39))/15). - Klaus Brockhaus, May 01 2010

Programs

Mathematica

PadRight[{},120,{1,2,3,4}] (* Harvey P. Dale, Aug 02 2016 *)

PARI

a(n)=(n-1)%4+1 \\ Charles R Greathouse IV, Jun 11 2015

Python

def A010883(n): return 1 + (n & 3) # Chai Wah Wu, May 25 2022

Formula

a(n) = 1 + (n mod 4). - Paolo P. Lava, Nov 21 2006

From Hieronymus Fischer, Jun 08 2007: (Start)

a(n) = A010873(n) + 1.

Also a(n) = (1/2)*(5 - (-1)^n - 2*(-1)^((2*n - 1 + (-1)^n)/4)).

G.f.: g(x) = (4*x^3 + 3*x^2 + 2*x + 1)/(1 - x^4) = (4*x^5 - 5*x^4 + 1)/((1 - x^4)*(1-x)^2). (End)

a(n) = 5/2 - cos(Pi*n/2) - sin(Pi*n/2) - (-1)^n/2. - R. J. Mathar, Oct 08 2011