A181778 - OEIS

A181778

Decimal expansion of root of (x+1)^sqrt(x) = sqrt(x)^(x+1).

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..123.

EXAMPLE

3.4892513116430665767127848980770651549163711326509817339662501...

MAPLE

Digits:=200:fsolve((x+1)^sqrt(x)-sqrt(x)^(x+1) =0, x, 0..10);

MATHEMATICA

RealDigits[x/.FindRoot[(x+1)^Sqrt[x]==(Sqrt[x])^(x+1), {x, 3}, WorkingPrecision -> 150]][[1]] (* Harvey P. Dale, Feb 17 2020 *)

PROG