A061508 Smallest positive m such that n^m has at least n digits.

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

Offset

1,2

Links

Table of n, a(n) for n=1..69.

Formula

a(n) = ceiling((n-1)/log_10(n)), n > 1. - Vladeta Jovovic, Dec 23 2001

Example

a(15) = 12, as 15^12 = 129746337890625 has 15 digits, while 15^11 = 8649755859375 has only 13 digits.

Maple

f := []: for i from 1 to 50 do for j from 1 do if length(i^j) >= i then f := [op(f), j]; break fi; od; od; op(f);

Mathematica

Join[{1}, Table[Ceiling[(n-1)/Log[10, n]], {n, 2, 70}]] (* Harvey P. Dale, Apr 14 2016 *)

Crossrefs

Sequence in context: A178400 A114458 A205842 * A120189 A157727 A374830

Adjacent sequences: A061505 A061506 A061507 * A061509 A061510 A061511

Keyword

base,nonn

Author

Amarnath Murthy, May 06 2001

Extensions

Corrected and extended by Asher Auel, May 14 2001

Offset corrected by Sean A. Irvine, Feb 18 2023

Status

approved