A049416 Largest number whose square has n digits.

3, 9, 31, 99, 316, 999, 3162, 9999, 31622, 99999, 316227, 999999, 3162277, 9999999, 31622776, 99999999, 316227766, 999999999, 3162277660, 9999999999, 31622776601, 99999999999, 316227766016, 999999999999, 3162277660168

Offset: 1

Author

Ulrich Schimke (ulrschimke(AT)aol.com)

Keywords

• nonn
• base
• easy
• nice

Comments

a(n) + A180416(n) + A180425(n) + A167615(n) = A002283(n).

Examples

			31^2 = 961, but 32^2 = 1024, hence a(3) = 31.
a(4) = 99: 99^2 = 9801 has 4 digits, while 100^2 = 10000 has 5 digits.
		

Links

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

Crossrefs

Cf. A061433, A049415. Equals A017936 - 1.

Programs

Magma

[Ceiling(Sqrt(10^n))-1: n in [1..30]]; // Vincenzo Librandi, Oct 01 2011

Mathematica

Ceiling[Sqrt[10^Range[40]]-1] (* Harvey P. Dale, Sep 30 2011 *)

Formula

a(n) = ceiling(sqrt(10^n)) - 1.

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 16 2001