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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 (list; graph; refs; listen; history; text; internal format)
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^n-1)^(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 * A018158 A057928 A026735

Adjacent sequences:  A114320 A114321 A114322 * A114324 A114325 A114326

KEYWORD

easy,nonn,base

AUTHOR

Jonathan Vos Post, Feb 06 2006

EXTENSIONS

Corrected data by Vincenzo Librandi, Oct 11 2011

STATUS

approved

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Last modified May 30 06:51 EDT 2017. Contains 287302 sequences.