A074153 Smallest n-digit power of n; or 0 if no such number exists.

1, 16, 243, 1024, 15625, 279936, 5764801, 16777216, 387420489, 1000000000, 25937424601, 743008370688, 1792160394037, 56693912375296, 129746337890625, 4503599627370496, 0, 374813367582081024, 0, 32768000000000000000, 0, 3011361496339065143296, 0

Offset

1,2

Comments

Zeros become more common as n increases. - Sean A. Irvine, Jan 12 2025

Links

Table of n, a(n) for n=1..23.

Formula

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

Mathematica

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 *)

Crossrefs

Cf. A074154.

Sequence in context: A231020 A274856 A064232 * A119933 A274753 A207995

Adjacent sequences: A074150 A074151 A074152 * A074154 A074155 A074156

Keyword

base,nonn

Author

Amarnath Murthy, Aug 29 2002

Extensions

More terms from Harvey P. Dale, Mar 04 2013

a(17) and a(19) corrected and more terms from Sean A. Irvine, Jan 12 2025

Status

approved