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Least n-expodigital number (i.e., numbers m such that m^n has exactly n decimal digits).
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%I #15 Jul 26 2017 03:12:19

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

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

%C 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.

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

%e 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.

%Y Cf. A102690.

%Y Essentially the same as A067471. - _R. J. Mathar_, Aug 30 2008

%K fini,full,nonn,base

%O 1,2

%A _Lekraj Beedassy_, Jan 21 2005

%E Edited by _Charles R Greathouse IV_, Aug 03 2010