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 A094214 Decimal expansion of 1/phi = phi - 1. 43
 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, 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, 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, 4 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Edge length of a regular decagon with unit circumradius. - Stanislav Sykora, May 07 2014 The value a+0i is the only invariant point of the complex-plane endomorphism M(z)=sqrt(2-sqrt(2+z)), and also its unique attractor, with the iterations converging exponentially from any starting complex value. Hence the infinite radical formula. - Stanislav Sykora, Apr 29 2016 LINKS Harry J. Smith, Table of n, a(n) for n = 0..20000 Aziz El Kacimi, Des triangles dorÃ©s, Images des MathÃ©matiques, CNRS, 2016 (in French). Eric Weisstein's World of Mathematics, GoldenRatioConjugate Eric Weisstein's World of Mathematics, Decagon FORMULA Equals sqrt(2-sqrt(2+sqrt(2-sqrt(2+ ...)))). - Stanislav Sykora, Apr 29 2016 From Christian Katzmann, Mar 19 2018: (Start) Equals Sum_{n>=0} (15*(2*n)!-8*n!^2)/(2*n!^2*3^(2*n+2)). Equals -1/2 + Sum_{n>=0} 5*(2*n)!/(2*n!^2*3^(2*n+1)). (End) EXAMPLE 0.6180339887498948482045868343656381177203091798057628621354486227052604628... MATHEMATICA RealDigits[N[GoldenRatio-1, 200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2011*) PROG (PARI) { default(realprecision, 20080); x=(sqrt(5)-1)/2; d=0; for (n=0, 20000, x=(x-d)*10; d=floor(x); write("b094214.txt", n, " ", d)); } \\ Harry J. Smith, Apr 19 2009 (PARI) (sqrt(5)-1)/2 \\ Michel Marcus, Mar 21 2016 CROSSREFS Cf. A001622, A104457. Sequence in context: A204205 A143019 A156921 * A001622 A186099 A021622 Adjacent sequences:  A094211 A094212 A094213 * A094215 A094216 A094217 KEYWORD cons,nonn,easy AUTHOR Cino Hilliard, May 27 2004 EXTENSIONS Edited by Eric W. Weisstein, Apr 17 2006 STATUS approved

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Last modified August 22 03:39 EDT 2018. Contains 313964 sequences. (Running on oeis4.)