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Largest number whose square has n digits.
9

%I #14 Feb 16 2022 23:56:01

%S 3,9,31,99,316,999,3162,9999,31622,99999,316227,999999,3162277,

%T 9999999,31622776,99999999,316227766,999999999,3162277660,9999999999,

%U 31622776601,99999999999,316227766016,999999999999,3162277660168

%N Largest number whose square has n digits.

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

%H Vincenzo Librandi, <a href="/A049416/b049416.txt">Table of n, a(n) for n = 1..1000</a>

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

%e 31^2 = 961, but 32^2 = 1024, hence a(3) = 31.

%e a(4) = 99: 99^2 = 9801 has 4 digits, while 100^2 = 10000 has 5 digits.

%t Ceiling[Sqrt[10^Range[40]]-1] (* _Harvey P. Dale_, Sep 30 2011 *)

%o (Magma) [Ceiling(Sqrt(10^n))-1: n in [1..30]]; // _Vincenzo Librandi_, Oct 01 2011

%Y Cf. A061433, A049415. Equals A017936 - 1.

%K nonn,base,easy,nice

%O 1,1

%A Ulrich Schimke (ulrschimke(AT)aol.com)

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