A114323 Largest number whose 5th power has n digits.
1, 2, 3, 6, 9, 15, 25, 39, 63, 99, 158, 251, 398, 630, 999, 1584, 2511, 3981, 6309, 9999, 15848, 25118, 39810, 63095, 99999, 158489, 251188, 398107, 630957, 999999, 1584893, 2511886, 3981071, 6309573, 9999999, 15848931, 25118864, 39810717
Offset: 1
Examples
a(3) = 3 because 3^5 = 243 which has 3 digits, while 4^5 = 1024 has 3 digits. a(32) = 2511886 because 2511886^5 = 99999914106500508412371346814176 has 32 digits, while 2511887^5 = 100000113160107495177704749808207 has 33 digits.
Links
- Georg Fischer, Table of n, a(n) for n = 1..300 [First 152 terms by Vincenzo Librandi]
Programs
-
Magma
[Ceiling((10^n)^(1/5))-1: n in [1..40]]; // Vincenzo Librandi, Oct 11 2011
-
Maple
seq(print(n, floor((10^n-1)^(1/5))), n=1..300); # Georg Fischer Apr 17 2024
-
Mathematica
Table[Floor[(10^n-1)^(1/5)],{n,40}] (* Harvey P. Dale, Dec 10 2012 *) -
PARI
a(n) = sqrtnint(10^n-1, 5) /* Georg Fischer on proposal of Michel Marcus, Apr 16 2024 */
Formula
a(n) = ceiling((10^n)^(1/5)) - 1.
Extensions
Data corrected by Vincenzo Librandi, Oct 11 2011
Comments