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A006266 A continued cotangent.
(Formerly M2073)
14
2, 14, 2786, 21624372014, 10111847525912679844192131854786, 1033930953043290626825587838528711318150300040875029341893199068078185510802565166824630504014 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The next (7th) term is 280 digits long. - M. F. Hasler, Oct 06 2014

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=1..6.

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

FORMULA

a(n+1) = a(n)^3 + 3*a(n) with a(1)=2.  a(n+1)=round((1+sqrt(2))^(3^n)). -  Artur Jasinski, Sep 24 2008, Corrected by M. F. Hasler, Oct 06 2014

MATHEMATICA

a = {}; k = 2; Do[AppendTo[a, k]; k = k^3 + 3 k, {n, 1, 10}]; a  (* or: *)

Table[Round[(1+Sqrt[2])^(3^n)], {n, 0, 10}] (* Artur Jasinski, Sep 24 2008 *)

PROG

(PARI) a(n, s=2)=for(i=2, n, s*=(s^2+3)); s \\ M. F. Hasler, Oct 06 2014

CROSSREFS

Cf. A006267. - Artur Jasinski, Sep 24 2008

Sequence in context: A277288 A296412 A296410 * A284378 A106484 A228342

Adjacent sequences:  A006263 A006264 A006265 * A006267 A006268 A006269

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Edited by M. F. Hasler, Oct 06 2014

STATUS

approved

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Last modified August 14 04:13 EDT 2020. Contains 336477 sequences. (Running on oeis4.)