

A114323


Largest number whose 5th power has n digits.


1



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
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OFFSET

1,2


COMMENTS

Note that the rightmost digit of n and n^5 are identical. This is to 5th powers as A061439 is to cubes and A049416 is to squares.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..300


FORMULA

a(n) = ceiling((10^n)^(1/5))  1.


EXAMPLE

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.


MATHEMATICA

Table[Floor[(10^n1)^(1/5)], {n, 40}] (* Harvey P. Dale, Dec 10 2012 *)


PROG

(PARI) a(n)=ceil(10^(n/5))1
(MAGMA) [Ceiling((10^n)^(1/5))1: n in [1..40]]; // Vincenzo Librandi, Oct 11 2011


CROSSREFS

Cf. A061439, A049416.
Sequence in context: A094993 A192671 A080239 * A293631 A018158 A057928
Adjacent sequences: A114320 A114321 A114322 * A114324 A114325 A114326


KEYWORD

easy,nonn,base


AUTHOR

Jonathan Vos Post, Feb 06 2006


EXTENSIONS

Data corrected by Vincenzo Librandi, Oct 11 2011


STATUS

approved



