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Numbers whose square has initial digit '9'.
3

%I #17 Nov 03 2021 13:03:56

%S 3,30,31,95,96,97,98,99,300,301,302,303,304,305,306,307,308,309,310,

%T 311,312,313,314,315,316,949,950,951,952,953,954,955,956,957,958,959,

%U 960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976

%N Numbers whose square has initial digit '9'.

%H Harvey P. Dale, <a href="/A045863/b045863.txt">Table of n, a(n) for n = 1..1000</a>

%t id9[n_]:=Module[{min=Floor[Sqrt[9*10^n]],max=Floor[Sqrt[10*10^n]]}, Select[ Range[ min,max], First[IntegerDigits[#^2]]==9&]]; Flatten[ Table[ id9[n],{n,0,5}]] (* _Harvey P. Dale_, May 29 2013 *)

%o (PARI) list(lim)=my(v=List()); for(d=1,2*#digits(lim\=1), for(n=sqrtint(9*10^(d-1)-1)+1, min(sqrtint(10^d-1), lim), listput(v, n))); Vec(v) \\ _Charles R Greathouse IV_, Nov 03 2021

%Y Cf. A045793.

%K nonn,base,easy

%O 1,1

%A _Jeff Burch_