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A104266 Largest n-digit square with no zero digits.

%I A104266 #40 Apr 01 2015 00:52:34
%S A104266 9,81,961,9216,99856,978121,9998244,99321156,999887641,9978811236,
%T A104266 99999515529,999332111556,9999995824729,99978881115136,
%U A104266 999999961946176,9999333211115556,99999999356895225,999978918111112681,9999999986285964964,99999333321111155556
%N A104266 Largest n-digit square with no zero digits.
%C A104266 See Formula section for exact formula for terms whose index n is divisible by 4, and upper bounds for other cases; see Links for additional information on those other cases. - _Jon E. Schoenfield_, Mar 30 2015
%H A104266 Jon E. Schoenfield, <a href="/A104266/b104266.txt">Table of n, a(n) for n = 1..100</a>
%H A104266 Jon E. Schoenfield, <a href="/A104266/a104266.txt">Odd-indexed terms with central digits aligned</a>
%H A104266 Jon E. Schoenfield, <a href="/A104266/a104266_4.txt">Patterns and upper bound for terms for which n mod 4 = 2</a>
%F A104266 From _Jon E. Schoenfield_, Mar 31 2015: (Start)
%F A104266 If n is divisible by 4, then a(n) = (10^(n/2) - ceiling(10^(n/4)/3))^2;
%F A104266 otherwise, if n is even, then a(n) < 10^(n) * (1 - (10^-((n-2)/4))* 2 / sqrt(90/1.000000000001026)) (see Links for derivation), except that a(2) = 81.
%F A104266 If n is odd, then a(n) ~ (floor(10^(n/2)))^2. (Although (floor(10*(n/2)))^2 gives an obvious upper bound for a(n) for all n, it seems to be a much tighter upper bound for odd values of n.) (End)
%e A104266 a(3) = Max{...., 729, 784, 841, 961} = 961.
%p A104266 f:= proc(n) local r;
%p A104266   r:= floor(sqrt(10^n));
%p A104266   while has(convert(r^2,base,10),0) do r:= r-1 od:
%p A104266 r^2
%p A104266 end proc:
%p A104266 seq(f(n),n=1..24); # _Robert Israel_, Mar 29 2015
%t A104266 f[n_] := Block[{k = Floor[ Sqrt[10^n]]}, While[ Union[ IntegerDigits[ k^2]][[1]] == 0, k-- ]; k^2]; Table[ f[n], {n, 18}] (* _Robert G. Wilson v_, Mar 03 2005 *)
%o A104266 (PARI) a(n)=k=floor(sqrt(10^n));while(k,if(type(k)=="t_INT"&&vecmin(digits(k^2)), return(k^2));k--)
%o A104266 vector(20,n,a(n)) \\ _Derek Orr_, Mar 29 2015
%Y A104266 Cf. A104265, A104264, A052041.
%K A104266 nonn,base
%O A104266 1,1
%A A104266 _Reinhard Zumkeller_, Feb 26 2005
%E A104266 More terms from _Robert G. Wilson v_, Mar 03 2005
%E A104266 More terms from _Jon E. Schoenfield_, Mar 29 2015