Search: id:A104457
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%I A104457
%S A104457 2,6,1,8,0,3,3,9,8,8,7,4,9,8,9,4,8,4,8,2,0,4,5,8,6,8,3,4,3,6,5,6,3,8,1,
%T A104457 1,7,7,2,0,3,0,9,1,7,9,8,0,5,7,6,2,8,6,2,1,3,5,4,4,8,6,2,2,7,0,5,2,6,0,
%U A104457 4,6,2,8,1,8,9,0,2,4,4,9,7,0,7,2,0,7,2,0,4,1,8,9,3,9,1,1,3,7,4,8
%N A104457 Decimal expansion of 1 + phi = 1 + Golden Ratio (cf. A001622).
%C A104457 Equivalently, decimal expansion of phi^2.
%C A104457 Only first term differs from the decimal expansion of Phi.
%C A104457 Zelo extends work of D. Roy by showing that the square of the golden 
               ratio is the optimal exponent of approximation by algebraic numbers 
               of degree 4 with bounded denominator and trace. [From Jonathan Vos 
               Post (jvospost3(AT)gmail.com), Mar 02 2009]
%D A104457 M. Berg, Phi, the golden ratio (to 4599 decimal places) and Fibonacci 
               numbers, Fibonacci Quarterly, 4 (1961), 157-162.
%D A104457 M. Livio, The Golden Ratio, Broadway Books, NY, 2002.
%D A104457 Damien Roy. Diophantine Approximation in Small Degree. Centre de Recherches 
               Mathematiques. CRM Proceedings and Lecture Notes. Volume 36 (2004), 
               269-285. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 02 
               2009]
%H A104457 Casey Mongoven, <a href="http://caseymongoven.com/catalogue/b12.html">
               Phi^2 number 1</a>; electronic music created using Phi^2.
%H A104457 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               FibonacciHyperbolicFunctions.html">Fibonacci Hyperbolic Functions</
               a>
%H A104457 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               ChromaticPolynomial.html">Chromatic Polynomial</a>
%H A104457 Dmitrij Zelo, <a href="http://arxiv.org/abs/0903.0086">Simultaneous Approximation 
               to Real and p-adic Numbers</a>, Feb 28, 2009. [From Jonathan Vos 
               Post (jvospost3(AT)gmail.com), Mar 02 2009]
%F A104457 Equals 2+A094214 = 1+A001622. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               May 19 2008
%e A104457 2.618033988...
%Y A104457 Cf. A001622.
%Y A104457 Sequence in context: A136766 A021386 A019679 this_sequence A155832 A136764 
               A136765
%Y A104457 Adjacent sequences: A104454 A104455 A104456 this_sequence A104458 A104459 
               A104460
%K A104457 nonn,cons,easy
%O A104457 1,1
%A A104457 Eric Weisstein (eric(AT)weisstein.com), Mar 08, 2005

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