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 A006266 A continued cotangent. (Formerly M2073) 14

%I M2073

%S 2,14,2786,21624372014,10111847525912679844192131854786,

%T 1033930953043290626825587838528711318150300040875029341893199068078185510802565166824630504014

%N A continued cotangent.

%C The next (7th) term is 280 digits long. - _M. F. Hasler_, Oct 06 2014

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

%H J. 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 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

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

%t Table[Round[(1+Sqrt[2])^(3^n)],{n,0,10}] (* _Artur Jasinski_, Sep 24 2008 *)

%o (PARI) a(n,s=2)=for(i=2,n,s*=(s^2+3));s \\ _M. F. Hasler_, Oct 06 2014

%Y Cf. A006267. - _Artur Jasinski_, Sep 24 2008

%K nonn

%O 1,1

%A _N. J. A. Sloane_.

%E Edited by _M. F. Hasler_, Oct 06 2014

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Last modified September 19 14:36 EDT 2020. Contains 337178 sequences. (Running on oeis4.)