0,2

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

Harry J. Smith, Table of n, a(n) for n=0,...,7

Eric Weisstein's World of Mathematics, Lehmer Cotangent Expansion

(1+sqrt(5))/2=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=(1+sqrt(5))/2, b(n)=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1)) then a(n)=floor(b(n)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 10 2003

a(n)=A000204(3^n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 18 2005

a(n)=Round[c^(3^n)] where c =GoldenRatio=1.6180339887498948482...=(Sqrt[5]+1)/2 [From Artur Jasinski (grafix(AT)csl.pl), Sep 22 2008]

Recurence a(n+1)=a(n)^3+a(n) a(0)=4 [From Artur Jasinski (grafix(AT)csl.pl), Sep 24 2008]

c = N[GoldenRatio, 1000]; Table[Round[c^(3^n)], {n, 1, 8}] [From Artur Jasinski (grafix(AT)csl.pl), Sep 22 2008]

a = {}; x = 4; Do[AppendTo[a, x]; x = x^3 + 3 x, {n, 1, 10}]; a [From Artur Jasinski (grafix(AT)csl.pl), Sep 24 2008]

(PARI) ?bn=vector(100); b(n)=if(n<0, 0, bn[n]); bn[1]=(1+sqrt(5))/2; ?for(n=2, 10, bn[n]=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1)))) ?a(n)=floor(b(n+1))

(PARI) { default(realprecision, 10000); bn=vector(8); bn[1]=(1+sqrt(5))/2; for(n=2, 8, bn[n]=(bn[n-1]*floor(bn[n-1]) + 1)/(bn[n-1] - floor(bn[n-1]))); for (n=1, 8, write("b006267.txt", n-1, " ", floor(bn[n]))); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 04 2009]

Cf. A002666, A002667, A002668.

Adjacent sequences: A006264 A006265 A006266 this_sequence A006268 A006269 A006270

Sequence in context: A118193 A052271 A080989 this_sequence A054951 A048957 A006425

nonn

N. J. A. Sloane (njas(AT)research.att.com).

The next term is too large to include.