A114322 Largest number whose 4th power has n digits.

1, 3, 5, 9, 17, 31, 56, 99, 177, 316, 562, 999, 1778, 3162, 5623, 9999, 17782, 31622, 56234, 99999, 177827, 316227, 562341, 999999, 1778279, 3162277, 5623413, 9999999, 17782794, 31622776, 56234132, 99999999, 177827941, 316227766, 562341325, 999999999, 1778279410

Offset: 1

Author

Jonathan Vos Post, Feb 06 2006

Keywords

• easy
• base
• nonn

Comments

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

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).

Examples

			a(10) = 316 because 316^4 = 9971220736 which has 10 digits, while 317^4 = 10098039121 has 11 digits.
a(35) = 562341325 because 562341325^4 = 99999999864602459914272843469140625 has 35 digits, while 562341326^4 = 100000000575914225104884587789852176 has 36.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A061439, A049416.

Programs

Magma

[Ceiling((10^n)^(1/4))-1: n in [1..40]]; // Vincenzo Librandi, Oct 01 2011

Mathematica

Ceiling[(10^Range[50])^(1/4)] - 1 (* Paolo Xausa, Jul 30 2024 *)

Formula

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