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%I #39 Feb 19 2024 01:51:24
%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
%H <a href="/index/Rec#order_04">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 From _Hieronymus Fischer_, Jun 08 2007: (Start)
%F a(n) = A010873(n) + 1.
%F Also a(n) = (1/2)*(5 - (-1)^n - 2*(-1)^((2n - 1 + (-1)^n)/4))).
%F 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)
%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
%o (Python)
%o def A010883(n): return 1 + (n & 3) # _Chai Wah Wu_, May 25 2022
%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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