This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A047273 #56 Jan 04 2025 02:41:18
%S A047273 0,1,3,5,6,7,9,11,12,13,15,17,18,19,21,23,24,25,27,29,30,31,33,35,36,
%T A047273 37,39,41,42,43,45,47,48,49,51,53,54,55,57,59,60,61,63,65,66,67,69,71,
%U A047273 72,73,75,77,78,79,81,83,84,85,87,89,90,91,93,95,96,97,99,101,102,103
%N A047273 Numbers that are congruent to {0, 1, 3, 5} mod 6.
%C A047273 Complement of A047235. - _Reinhard Zumkeller_, Oct 01 2008
%H A047273 Reinhard Zumkeller, <a href="/A047273/b047273.txt">Table of n, a(n) for n = 1..1000</a>
%H A047273 <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>.
%H A047273 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-1).
%F A047273 G.f.: x*(1+x+x^2)/((1-x)^2*(1+x^2)) = x*(1-x^2)*(1-x^3)/((1-x)^3*(1-x^4)).
%F A047273 a(n) = n + A004524(n+1) = -a(-n) for all n in Z.
%F A047273 Starting (1, 3, 5, ...) = partial sums of (1, 2, 2, 1, 1, 2, 2, 1, 1, ...). - _Gary W. Adamson_, Jun 19 2008
%F A047273 A093719(a(n)) = 1. - _Reinhard Zumkeller_, Oct 01 2008
%F A047273 a(n) = 2*(n-floor(n/4)) - (3-I^n-(-I)^n-(-1)^n)/4, with offset 0..a(0)=0. - _Gary Detlefs_, Mar 19 2010
%F A047273 a(n) = (3*n-3+cos(Pi*n/2))/2. - _R. J. Mathar_, Oct 08 2010
%F A047273 From _Wesley Ivan Hurt_, May 20 2016: (Start)
%F A047273 a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-a(n-4) for n>4.
%F A047273 a(n) = (6*n-6+(-1)^(n/2)+(-1)^(-n/2))/4. (End)
%F A047273 Euler transform of length 4 sequence [3, -1, -1, 1]. - _Michael Somos_, Jun 24 2017
%F A047273 Sum_{n>=2} (-1)^n/a(n) = log(2)/3 + log(3)/2. - _Amiram Eldar_, Dec 16 2021
%F A047273 E.g.f.: (2 + 3*exp(x)*(x - 1) + cos(x))/2. - _Stefano Spezia_, Jul 26 2024
%p A047273 seq(2*(n-floor(n/4)) - (3-I^n-(-I)^n-(-1)^n)/4, n = 0..69); # _Gary Detlefs_, Mar 19 2010
%t A047273 LinearRecurrence[{2,-2,2,-1},{0,1,3,5},80] (* _Harvey P. Dale_, Jan 04 2015 *)
%o A047273 (PARI) a(n)=n+(n+1)\4+(n+2)\4
%o A047273 (Sage) [(lucas_number1(n+2, 0, 1)+3*n)/2 for n in range(0, 70)] # _Zerinvary Lajos_, Mar 09 2009
%o A047273 (Haskell)
%o A047273 a047273 n = a047273_list !! (n-1)
%o A047273 a047273_list = 0 : 1 : 3 : 5 : map (+ 6) a047273_list
%o A047273 -- _Reinhard Zumkeller_, Feb 19 2013
%o A047273 (Magma) [(6*n-6+(-1)^(n div 2)+(-1)^(-n div 2))/4: n in [1..100]]; // _Wesley Ivan Hurt_, May 20 2016
%Y A047273 Cf. A004524, A007310, A047228, A047235, A047241, A047261, A093719, A096981.
%Y A047273 First differences of A281026.
%Y A047273 See A301729 for an essentially identical sequence.
%K A047273 nonn,easy
%O A047273 1,3
%A A047273 _N. J. A. Sloane_