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A094214 Decimal expansion of 1/phi = phi - 1. 42
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 dorés, Images des Mathématiques, 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

EXAMPLE

0.618033988749894848204586834...

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 December 11 21:15 EST 2017. Contains 295919 sequences.