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%I A047202 #44 Apr 16 2023 03:16:53
%S A047202 2,3,4,7,8,9,12,13,14,17,18,19,22,23,24,27,28,29,32,33,34,37,38,39,42,
%T A047202 43,44,47,48,49,52,53,54,57,58,59,62,63,64,67,68,69,72,73,74,77,78,79,
%U A047202 82,83,84,87,88,89,92,93,94,97,98,99,102,103,104,107,108
%N A047202 Numbers that are congruent to {2, 3, 4} mod 5.
%H A047202 Stefano Spezia, <a href="/A047202/b047202.txt">Table of n, a(n) for n = 1..10000</a>
%H A047202 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A047202 G.f.: x*(2+x+x^2+x^3) / ((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Oct 07 2011
%F A047202 From _Wesley Ivan Hurt_, Jun 14 2016: (Start)
%F A047202 a(n) = a(n-1) + a(n-3) - a(n-4) for n>3.
%F A047202 a(n) = (15*n-3-6*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9.
%F A047202 a(3k) = 5k-1, a(3k-1) = 5k-2, a(3k-2) = 5k-3. (End)
%F A047202 a(n) = 2*n - floor((n-1)/3) - ((n-1) mod 3). - _Wesley Ivan Hurt_, Sep 26 2017
%F A047202 Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt((5+sqrt(5))/10)*Pi/5 + log(phi)/sqrt(5) - 3*log(2)/5, where phi is the golden ratio (A001622). - _Amiram Eldar_, Apr 16 2023
%p A047202 A047202:=n->(15*n-3-6*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047202(n), n=1..100); # _Wesley Ivan Hurt_, Jun 14 2016
%t A047202 Select[Range[0, 200], MemberQ[{2, 3, 4}, Mod[#, 5]] &] (* _Vladimir Joseph Stephan Orlovsky_, Feb 12 2012 *)
%o A047202 (Magma) [n: n in [1..150] | n mod 5 in [2..4]]; // _Vincenzo Librandi_, Mar 31 2011
%o A047202 (PARI) a(n)=n\3*5+[-1,2,3][n%3+1] \\ _Charles R Greathouse IV_, Dec 22 2011
%Y A047202 Cf. A001622.
%K A047202 nonn,easy
%O A047202 1,1
%A A047202 _N. J. A. Sloane_

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