A102691 Least n-expodigital number (i.e., numbers m such that m^n has exactly n decimal digits).

0, 4, 5, 6, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

Offset: 1

Author

Lekraj Beedassy, Jan 21 2005

Keywords

• fini
• full
• nonn
• base

Comments

10^(n-1) being the smallest n-digit number, n-expodigital numbers exist iff 10^(n-1) < 9^n, i.e., iff n-1 < n*log_10(9); this condition holds for all n up to 21 because beyond we have, for instance, 20 < 22*log_10(9) < 21. Thus numbers can be at most 21-expodigital.

Examples

			a(3)=5 because this is the first number followed by 6,7,8 and 9 which are all 3-expodigital: 5^3 = 125; 6^3 = 216; 7^3 = 343; 8^3 = 512; 9^3 = 729.
		

Crossrefs

Cf. A102690.

Essentially the same as A067471. - R. J. Mathar, Aug 30 2008

Formula

a(n) = 10 - A102690(n).

Extensions

Edited by Charles R Greathouse IV, Aug 03 2010