Search: id:A006267
Results 1-1 of 1 results found.

%I A006267 M3699
%S A006267 1,4,76,439204,84722519070079276,
%T A006267 608130213374088941214747405817720942127490792974404
%N A006267 Continued cotangent for the golden ratio.
%D A006267 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006267 Shallit, Jeffrey; Predictable regular continued cotangent expansions. 
               J. Res. Nat. Bur. Standards Sect. B 80B (1976), no. 2, 285-290.
%H A006267 Harry J. Smith, <a href="b006267.txt">Table of n, a(n) for n=0,...,7</
               a>
%H A006267 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LehmerCotangentExpansion.html">Lehmer Cotangent Expansion</a>
%F A006267 (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
%F A006267 a(n)=A000204(3^n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 18 
               2005
%F A006267 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]
%F A006267 Recurence a(n+1)=a(n)^3+a(n) a(0)=4 [From Artur Jasinski (grafix(AT)csl.pl), 
               Sep 24 2008]
%t A006267 c = N[GoldenRatio, 1000]; Table[Round[c^(3^n)], {n, 1, 8}] [From Artur 
               Jasinski (grafix(AT)csl.pl), Sep 22 2008]
%t A006267 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]
%o A006267 (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))
%o A006267 (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]
%Y A006267 Cf. A002666, A002667, A002668.
%Y A006267 Sequence in context: A118193 A052271 A080989 this_sequence A054951 A048957 
               A006425
%Y A006267 Adjacent sequences: A006264 A006265 A006266 this_sequence A006268 A006269 
               A006270
%K A006267 nonn
%O A006267 0,2
%A A006267 N. J. A. Sloane (njas(AT)research.att.com).
%E A006267 The next term is too large to include.

Search completed in 0.001 seconds