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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 (list; graph; refs; listen; history; text; internal format)
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))-1-1/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: A245434 A051512 A079668 * A260510 A125291 A055187

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

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Last modified March 29 21:48 EDT 2017. Contains 284288 sequences.