

A144211


Decimal expansion of solution to (x+1)^(x+1) = x^(x+2).


1



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

1,1


COMMENTS

Decimal expansion of the convergent to x = 1/(x^(1/(x+1))1) for x > 1.
Also the decimal expansion of a solution to 1/(x^(1/(x+1))1)x. The other solution is 1.
Perhaps Pi  3.1410415254107... = 0.0005511281790... has a generating function.
Some experimentation will show that the recurrence
x = 1/(x^(1/(x+1))11/x^8.446) converges to 3.14159264313...
Equals A100086 minus 1. [From R. J. Mathar, Jun 25 2010]


LINKS

Table of n, a(n) for n=1..99.


EXAMPLE

3.141041525410788500945231446733515159979856852445599488196546631496424\
113176486717028008922619733816396791510643825934571540309860365903143378\
733054296284455377...


PROG

(PARI) y=solve(x=3, 4, 1/(x^(1/(x+1))1)x); a=eval(Vec(Str(y*10^99)));
for(j=1, 99, print1(a[j]", "))


CROSSREFS

Sequence in context: A305100 A051512 A079668 * A260510 A125291 A320640
Adjacent sequences: A144208 A144209 A144210 * A144212 A144213 A144214


KEYWORD

base,nonn


AUTHOR

Cino Hilliard, Sep 14 2008


EXTENSIONS

Made comment more precise  R. J. Mathar, Jun 25 2010
Edited by N. J. A. Sloane, Jul 05 2010


STATUS

approved



