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A006268 A continued cotangent.
(Formerly M3141)
12
3, 36, 46764, 102266868132036, 1069559300034650646049671039050649693658764 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

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

LINKS

Table of n, a(n) for n=0..4.

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

FORMULA

From Artur Jasinski, Oct 03 2008: (Start)

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

a(n) = round((3/2 + sqrt(13)/2)^(3^(n - 1))). (End)

MATHEMATICA

a = {}; k = 3; Do[AppendTo[a, k]; k = k^3 + 3 k, {n, 1, 6}]; a (* Artur Jasinski, Oct 03 2008 *)

Table[Round[N[(3/2 + Sqrt[13]/2)^(3^(n - 1)), 1000]], {n, 1, 8}] (* Artur Jasinski, Oct 03 2008 *)

PROG

(PARI) a(n) = if (n==0, 3, a(n-1)^3 + 3*a(n-1)); \\ Michel Marcus, Aug 28 2020

CROSSREFS

Sequence in context: A262825 A088322 A080807 * A264842 A210508 A073236

Adjacent sequences:  A006265 A006266 A006267 * A006269 A006270 A006271

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified September 26 16:43 EDT 2020. Contains 337374 sequences. (Running on oeis4.)