A095703 Integer part of the (positive) solution to x^x = 10^n.

1, 2, 3, 4, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 12, 13, 13, 14, 15, 15, 16, 17, 17, 18, 18, 19, 19, 20, 21, 21, 22, 22, 23, 23, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37, 38, 38, 39, 39, 40, 40, 41, 41

Offset: 0

Author

Cino Hilliard, Jul 06 2004

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 1001 terms from Andrew Howroyd)

Crossrefs

Cf. A066022, A086858.

Programs

Maple

a:= n-> `if`(n=0, 1, (t-> floor(t/LambertW(t)))(n*log(10))):
seq(a(n), n=0..80);  # Alois P. Heinz, Nov 07 2019

PARI

a(n) = floor(solve(x=1, max(10,n+1), x^x-10^n))

PARI

a(n) = {my(k=1); while(k^k <= 10^n, k++); k-1} \\ Andrew Howroyd, Nov 07 2019

Formula

a(n) = n*log(10)/LambertW(n*log(10)) for n > 0, a(0) = 1. - Alois P. Heinz, Nov 07 2019

Extensions

Terms a(23) and beyond from Andrew Howroyd, Nov 07 2019