A006269 - OEIS

%I M4028 #16 Aug 28 2020 06:15:18

%S 5,140,2744420,20670535451567121260,

%T 8831921094058107711185956797335984862612406515067837739780

%N A continued cotangent.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Jeffrey Shallit, <a href="http://archive.org/details/jresv80Bn2p285">Predictable regular continued cotangent expansions</a>, J. Res. Nat. Bur. Standards Sect. B 80B (1976), no. 2, 285-290.

%F From _Artur Jasinski_, Oct 03 2008: (Start)

%F Recurrence: a(n+1)=a(n)^3+3*a(n) and a(0)=5.

%F a(n) = round((5/2 + sqrt(29)/2)^(3^(n - 1))). (End)

%t a = {}; k = 5; Do[AppendTo[a, k]; k = k^3 + 3 k, {n, 1, 8}]; a (* _Artur Jasinski_, Oct 03 2008 *)

%t Table[Round[(5/2 + Sqrt[29]/2)^(3^(n - 1))], {n, 1, 8}] (* _Artur Jasinski_, Oct 03 2008 *)

%t NestList[#^3+3#&,5,5] (* _Harvey P. Dale_, Feb 14 2013 *)

%K nonn

%O 0,1

%A _N. J. A. Sloane_.