

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 complexplane endomorphism M(z)=sqrt(2sqrt(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(2sqrt(2+sqrt(2sqrt(2+ ...)))).  Stanislav Sykora, Apr 29 2016


EXAMPLE

0.618033988749894848204586834...


MATHEMATICA

RealDigits[N[GoldenRatio1, 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=(xd)*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



