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 A114323 Largest number whose 5th power has n digits. 1

%I

%S 1,2,3,6,9,15,25,39,63,99,158,251,398,630,999,1584,2511,3981,6309,

%T 9999,15848,25118,39810,63095,99999,158489,251188,398107,630957,

%U 999999,1584893,2511886,3981071,6309573,9999999,15848931,25118864,39810717

%N Largest number whose 5th power has n digits.

%C 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.

%H Vincenzo Librandi, <a href="/A114323/b114323.txt">Table of n, a(n) for n = 1..300</a>

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

%e a(3) = 3 because 3^5 = 243 which has 3 digits, while 4^5 = 1024 has 3 digits.

%e a(32) = 2511886 because 2511886^5 = 99999914106500508412371346814176 has 32 digits, while 2511887^5 = 100000113160107495177704749808207 has 33 digits.

%t Table[Floor[(10^n-1)^(1/5)],{n,40}] (* _Harvey P. Dale_, Dec 10 2012 *)

%o (PARI) a(n)=ceil(10^(n/5))-1

%o (MAGMA) [Ceiling((10^n)^(1/5))-1: n in [1..40]]; // _Vincenzo Librandi_, Oct 11 2011

%Y Cf. A061439, A049416.

%K easy,nonn,base

%O 1,2

%A _Jonathan Vos Post_, Feb 06 2006

%E Data corrected by _Vincenzo Librandi_, Oct 11 2011

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Last modified November 22 02:58 EST 2019. Contains 329383 sequences. (Running on oeis4.)