

A124930


Decimal expansion of the unique positive real root of the equation x^x = x + 1.


0



1, 7, 7, 6, 7, 7, 5, 0, 4, 0, 0, 9, 7, 0, 5, 4, 6, 9, 7, 4, 7, 9, 7, 3, 0, 7, 4, 4, 0, 3, 8, 7, 5, 6, 7, 4, 8, 6, 3, 7, 4, 1, 1, 0, 3, 4, 3, 2, 9, 2, 9, 6, 1, 3, 9, 0, 8, 4, 3, 7, 4, 0, 1, 5, 2, 7, 3, 1, 1, 8, 6, 5, 8, 9, 3, 2, 8, 2, 4, 7, 7, 0, 7, 0, 2, 0, 7, 2, 7, 8, 6, 1, 5, 1, 3, 1, 3, 5, 2, 3, 6, 3, 0, 0, 9
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OFFSET

1,2


COMMENTS

The proof by R. P. Stanley using contradiction and the GelfondSchneider Theorem shows that this number is transcendental.
Let r be this constant and f(x) be the function x^(1/(r1)). Since r^(r1) = 1 + 1/r, we have r = f(1 + 1/f(1 + 1/f(1 + 1/f(1 + ...)))).  Gerald McGarvey, Jan 12 2008


REFERENCES

R. P. Stanley, "A transcendental number?: Quickie 8810", Mathematical Entertainments column (Steven H. Weintraub editor), The Mathematical Intelligencer, vol. 11, no. 1, Winter 1989, p. 55.


LINKS

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


EXAMPLE

1.77677504009705469747973074403...


PROG

(PARI) solve(x=1, 2, x^xx1)


CROSSREFS

Sequence in context: A019765 A280507 A059965 * A195202 A252799 A109939
Adjacent sequences: A124927 A124928 A124929 * A124931 A124932 A124933


KEYWORD

cons,nonn


AUTHOR

Rick L. Shepherd, Nov 12 2006


STATUS

approved



