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%I #15 Jan 13 2025 02:30:00
%S 1,16,243,1024,15625,279936,5764801,16777216,387420489,1000000000,
%T 25937424601,743008370688,1792160394037,56693912375296,
%U 129746337890625,4503599627370496,0,374813367582081024,0,32768000000000000000,0,3011361496339065143296,0
%N Smallest n-digit power of n; or 0 if no such number exists.
%C Zeros become more common as n increases. - _Sean A. Irvine_, Jan 12 2025
%F For n >= 2, a(n) = ceiling((n-1)/log_10(n)), if ceiling((n-1)/log_10(n)) < ceiling(n/log_10(n)), and 0 otherwise. - _Amiram Eldar_, Jan 13 2025
%t a[n_] := Module[{e1 = Ceiling[(n-1) * Log[n, 10]], e2 = Ceiling[n * Log[n, 10]]}, If[e1 == e2, 0, n^e1]]; a[1] = 1; Array[a, 23] (* _Harvey P. Dale_, Mar 04 2013, corrected by _Amiram Eldar_, Jan 13 2025 *)
%Y Cf. A074154.
%K base,nonn
%O 1,2
%A _Amarnath Murthy_, Aug 29 2002
%E More terms from _Harvey P. Dale_, Mar 04 2013
%E a(17) and a(19) corrected and more terms from _Sean A. Irvine_, Jan 12 2025