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Largest number whose 4th power has n digits.
19

%I #19 Jul 30 2024 16:44:58

%S 1,3,5,9,17,31,56,99,177,316,562,999,1778,3162,5623,9999,17782,31622,

%T 56234,99999,177827,316227,562341,999999,1778279,3162277,5623413,

%U 9999999,17782794,31622776,56234132,99999999,177827941,316227766,562341325,999999999,1778279410

%N Largest number whose 4th power has n digits.

%C This is to 4th powers as A061439 is to cubes and A049416 is to squares.

%C a(n) + A186649(n) + A186651(n) + A186653(n) + A186655(n) + A186657(n) + A186659(n) + A186661(n) + A186663(n) + A186665(n) + A186667(n) + A186669(n) + A186671(n) + A186673(n) + A186675(n) + A186677(n) + A186680(n) + A186682(n) + A186684(n) = A002283(n).

%H Vincenzo Librandi, <a href="/A114322/b114322.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = ceiling((10^n)^(1/4)) - 1.

%e a(10) = 316 because 316^4 = 9971220736 which has 10 digits, while 317^4 = 10098039121 has 11 digits.

%e a(35) = 562341325 because 562341325^4 = 99999999864602459914272843469140625 has 35 digits, while 562341326^4 = 100000000575914225104884587789852176 has 36.

%t Ceiling[(10^Range[50])^(1/4)] - 1 (* _Paolo Xausa_, Jul 30 2024 *)

%o (Magma) [Ceiling((10^n)^(1/4))-1: n in [1..40]]; // _Vincenzo Librandi_, Oct 01 2011

%Y Cf. A061439, A049416.

%K easy,base,nonn

%O 1,2

%A _Jonathan Vos Post_, Feb 06 2006