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A010883 Simple periodic sequence: repeat 1,2,3,4. 7

%I

%S 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,

%T 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,

%U 1,2,3,4,1,2,3,4,1,2,3,4,1

%N Simple periodic sequence: repeat 1,2,3,4.

%C Partial sums are given by A130482(n)+n+1. - _Hieronymus Fischer_, Jun 08 2007

%C 1234/9999=0,123412341234... - _Eric Desbiaux_, Nov 03 2008

%C Terms of the simple continued fraction of 5/(2*sqrt(39)-9). - _Paolo P. Lava_, Feb 16 2009

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).

%F a(n) = 1 + (n mod 4) - _Paolo P. Lava_, Nov 21 2006

%F a(n)=A010873(n)+1. Also a(n)=1/2*(5-(-1)^n-2*(-1)^((2n-1+(-1)^n)/4))). G.f.: g(x)=(4x^3+3x^2+2x+1)/(1-x^4)=(4x^5-5x^4+1)/((1-x^4)(1-x)^2). - _Hieronymus Fischer_, Jun 08 2007

%F a(n) = (7*(n mod 4)+(n+1 mod 4)+(n+2 mod 4)+(n+3 mod 4))/6 (cf. forms of modular arithmetic of Paolo P. Lava, i.e. see A146094). - _Bruno Berselli_, Sep 27 2010

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

%t PadRight[{},120,{1,2,3,4}] (* _Harvey P. Dale_, Aug 02 2016 *)

%o (PARI) a(n)=(n-1)%4+1 \\ _Charles R Greathouse IV_, Jun 11 2015

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

%Y Cf. A177037 (decimal expansion of (9+2*sqrt(39))/15). - _Klaus Brockhaus_, May 01 2010

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.

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Last modified October 16 03:37 EDT 2019. Contains 328040 sequences. (Running on oeis4.)