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...
FORMULA
Equals A100086 minus 1. - R. J. Mathar, Jun 25 2010
EXAMPLE
3.14104152541078850094523144673351515997985685244559...
MATHEMATICA
RealDigits[x /. FindRoot[(x + 1)^(x + 1) == x^(x + 2), {x, 3}, WorkingPrecision -> 120]][[1]] (* Amiram Eldar, Feb 24 2024 *)
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
KEYWORD
nonn,cons
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