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A085848 Decimal expansion of Foias' Constant. 0
1, 1, 8, 7, 4, 5, 2, 3, 5, 1, 1, 2, 6, 5, 0, 1, 0, 5, 4, 5, 9, 5, 4, 8, 0, 1, 5, 8, 3, 9, 6, 5, 1, 9, 3, 5, 1, 2, 1, 5, 6, 9, 2, 6, 8, 1, 5, 8, 5, 8, 6, 0, 3, 5, 3, 0, 1, 0, 1, 0, 4, 1, 2, 6, 1, 9, 8, 7, 8, 0, 4, 1, 8, 7, 2, 3, 5, 2, 5, 4, 0, 7, 3, 8, 7, 0, 2, 4, 6, 5, 7, 6, 0, 6, 0, 8, 6, 5, 7, 9, 4, 3, 3, 7, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

This is the unique real x_1 such that iterating x_{n+1} = (1 + 1/x_n)^n yields a series which diverges to infinity (rather than having 1 and infinity as limit points). - Charles R Greathouse IV, Nov 19 2013

LINKS

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Foias Constant

Wikipedia, Foias Constant

FORMULA

  x_{n+1} = (1 + 1/{x_n})^n for n=1,2,3,...

EXAMPLE

1.18745235112650105459548015839651935121569268158586035301010412619878...

MATHEMATICA

x[1, a_] = a; x[n_, a_] :=(1+1/x[n-1, a])^(n-1); RealDigits[ a /. FindRoot[x[220, a] == 10^65, {a, 1, 2}, WorkingPrecision -> 110, MaxIterations -> 500]][[1]][[1 ;; 105]] (* Jean-Fran├žois Alcover, Nov 12 2012 *)

PROG

(PARI) f(x, n)=for(i=2, n, x=(1.0+1.0/x)^(i-1)); return(x) default(realprecision, 200); solve(y=1, 2, f(y, 800)-1-10^(-200)) \\ Robert Gerbicz, May 08 2008

CROSSREFS

Sequence in context: A196914 A072102 A154815 * A008960 A077744 A111448

Adjacent sequences:  A085845 A085846 A085847 * A085849 A085850 A085851

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Jul 05, 2003

EXTENSIONS

More terms from Robert Gerbicz, May 08 2008

STATUS

approved

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Last modified October 21 04:50 EDT 2014. Contains 248373 sequences.