A144211 Decimal expansion of solution to (x+1)^(x+1) = x^(x+2).

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

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...

Links

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

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

Cf. A100086.

Sequence in context: A305100 A051512 A079668 * A260510 A125291 A320640

Adjacent sequences: A144208 A144209 A144210 * A144212 A144213 A144214

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