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 A144437 #47 Dec 12 2023 08:20:58
%S A144437 3,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3,
%T A144437 3,1,3,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3,3,
%U A144437 1,3,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3,3
%N A144437 Period 3: repeat [3, 3, 1].
%C A144437 The sequence is generated from numerators in the energy differences of the hydrogen spectrum: A005563(1), A061037(4), A061039(6), A061041(8), A061043(10), A061045(12), A061047(14), A061049(16), ...
%C A144437 Conjecture: a(n) is the separatix. See A045944.
%C A144437 Also the decimal expansion of the constant 3310/999. - _R. J. Mathar_, May 21 2009
%C A144437 Continued fraction expansion of A171417.
%C A144437 Greatest common divisor of (n+1)^2-1 and (n+1)^2+2. - _Bruno Berselli_, Mar 08 2017
%H A144437 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%F A144437 a(n) = (7-4*cos(2*Pi*n/3))/3. - _Jaume Oliver Lafont_, Nov 23 2008
%F A144437 G.f.: x*(3 + 3*x + x^2)/((1 - x)*(1 + x + x^2)). - _R. J. Mathar_, May 21 2009
%F A144437 a(n) = 3/gcd(n,3). - _Reinhard Zumkeller_, Oct 30 2009
%F A144437 a(n) = denominator(n^k/3), where k>0 is an integer. - _Enrique Pérez Herrero_, Oct 05 2011
%F A144437 a(n) = gcd(T(n+1), T(2)) = A256095(n+1, 2), with the triangular numbers T = A000217, for n >= 1. - _Wolfdieter Lang_, Mar 17 2015
%F A144437 a(n) = a(n-3) for n>3; a(n) = A169609(n) for n>0. - _Wesley Ivan Hurt_, Jul 02 2016
%F A144437 E.g.f.: (1/3)*(7*exp(x) - 4*exp(-x/2)*cos(sqrt(3)*x/2) - 3). - _G. C. Greubel_, Aug 24 2017
%F A144437 From _Nicolas Bělohoubek_, Nov 11 2021: (Start)
%F A144437 a(n) = 9/(a(n-2)*a(n-1)).
%F A144437 a(n) = 7 - a(n-2) - a(n-1). See also A052901 or A069705. (End)
%p A144437 seq(op([3, 3, 1]), n=1..50); # _Wesley Ivan Hurt_, Jul 02 2016
%t A144437 A144437[n_]:=Denominator[n/3]; Array[A144437,100] (* _Enrique Pérez Herrero_, Oct 05 2011 *)
%t A144437 CoefficientList[Series[(3 + 3 x + x^2)/(1 - x^3), {x, 0, 120}], x] (* _Michael De Vlieger_, Jul 02 2016 *)
%t A144437 Table[Mod[2*n^2 + 1, 3,1], {n,1,50}] (* _G. C. Greubel_, Aug 24 2017 *)
%o A144437 (PARI) a(n)=if(n%3,3,1) \\ _Charles R Greathouse IV_, Sep 28 2015
%o A144437 (Magma) &cat [[3, 3, 1]^^30]; // _Wesley Ivan Hurt_, Jul 02 2016
%Y A144437 Cf. A000217, A045944, A109007, A164306, A167192, A169609, A256095.
%Y A144437 Numerators in the energy differences of the hydrogen spectrum: A005563(1), A061037(4), A061039(6), A061041(8), A061043(10), A061045(12), A061047(14), A061049(16), ...
%K A144437 nonn,easy
%O A144437 1,1
%A A144437 _Paul Curtz_, Oct 05 2008
%E A144437 Edited by _R. J. Mathar_, May 21 2009