A006269 A continued cotangent.

5, 140, 2744420, 20670535451567121260, 8831921094058107711185956797335984862612406515067837739780

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

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

Links

• Jeffrey Shallit, Predictable regular continued cotangent expansions, J. Res. Nat. Bur. Standards Sect. B 80B (1976), no. 2, 285-290.

Programs

Mathematica

a = {}; k = 5; Do[AppendTo[a, k]; k = k^3 + 3 k, {n, 1, 8}]; a (* Artur Jasinski, Oct 03 2008 *)
Table[Round[(5/2 + Sqrt[29]/2)^(3^(n - 1))], {n, 1, 8}] (* Artur Jasinski, Oct 03 2008 *)
NestList[#^3+3#&,5,5] (* Harvey P. Dale, Feb 14 2013 *)

Formula

From Artur Jasinski, Oct 03 2008: (Start)

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

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