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A085846 Decimal expansion of root of x = (1+1/x)^x. 8
2, 2, 9, 3, 1, 6, 6, 2, 8, 7, 4, 1, 1, 8, 6, 1, 0, 3, 1, 5, 0, 8, 0, 2, 8, 2, 9, 1, 2, 5, 0, 8, 0, 5, 8, 6, 4, 3, 7, 2, 2, 5, 7, 2, 9, 0, 3, 2, 7, 1, 2, 1, 2, 4, 8, 5, 3, 7, 7, 1, 0, 3, 9, 6, 1, 6, 8, 5, 0, 6, 4, 8, 8, 0, 0, 9, 1, 5, 7, 7, 4, 3, 6, 2, 9, 0, 4, 2, 0, 1, 3, 8, 0, 4, 8, 2, 8, 2, 5, 6, 6, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Equivalently, the root of x^(x+1) = (x+1)^x.

Contribution from Cino Hilliard, Sep 13 2008: (Start)

Also a root of 1/(x^(1/x)-1) - x = 0 and 1/(x^(1/x)-1/x-1) - x = 0 which also contains

the root 5.50798565277317825758902... 1/(x^(1/x)-1) ~ Pi(x) and

1/(x^(1/x)-1/x-1) ~ Pi(x) which is a much better approximation. These roots also

can be computed by the recurrences x = 1/(x^(1/x)-1) and x = 1/(x^(1/x)-1/x-1). (End)

LINKS

Table of n, a(n) for n=1..102.

Eric Weisstein's World of Mathematics, Foias Constant

FORMULA

x^(1/x)=(x+1)^(1/(x+1)) where x equals 2.2931662.... - Marco Matosic, Nov 25 2005

EXAMPLE

2.2931662874118610315080282912508058643722572903271212485377103961...

MATHEMATICA

RealDigits[ FindRoot[x^(1/x) - (x + 1)^(1/(x + 1)) == 0, {x, 2}, WorkingPrecision -> 128][[1, 2]], 10, 111][[1]] (* Robert G. Wilson v *)

PROG

(PARI) solve(x=2, 3, (1+1/x)^x-x) \\ Charles R Greathouse IV, Apr 14 2014

CROSSREFS

Cf. A021002, A169862.

Sequence in context: A182106 A011403 A113554 * A021440 A157216 A020776

Adjacent sequences:  A085843 A085844 A085845 * A085847 A085848 A085849

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Jul 05, 2003

STATUS

approved

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Last modified October 22 02:31 EDT 2014. Contains 248381 sequences.