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 A104266 Largest n-digit square with no zero digits. 3
 9, 81, 961, 9216, 99856, 978121, 9998244, 99321156, 999887641, 9978811236, 99999515529, 999332111556, 9999995824729, 99978881115136, 999999961946176, 9999333211115556, 99999999356895225, 999978918111112681, 9999999986285964964, 99999333321111155556 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 LINKS Jon E. Schoenfield, Table of n, a(n) for n = 1..100 Jon E. Schoenfield, Odd-indexed terms with central digits aligned Jon E. Schoenfield, Patterns and upper bound for terms for which n mod 4 = 2 FORMULA From Jon E. Schoenfield, Mar 31 2015: (Start) If n is divisible by 4, then a(n) = (10^(n/2) - ceiling(10^(n/4)/3))^2; 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. 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) EXAMPLE a(3) = Max{...., 729, 784, 841, 961} = 961. MAPLE f:= proc(n) local r;   r:= floor(sqrt(10^n));   while has(convert(r^2, base, 10), 0) do r:= r-1 od: r^2 end proc: seq(f(n), n=1..24); # Robert Israel, Mar 29 2015 MATHEMATICA f[n_] := Block[{k = Floor[ Sqrt[10^n]]}, While[ Union[ IntegerDigits[ k^2]][] == 0, k-- ]; k^2]; Table[ f[n], {n, 18}] (* Robert G. Wilson v, Mar 03 2005 *) PROG (PARI) a(n)=k=floor(sqrt(10^n)); while(k, if(type(k)=="t_INT"&&vecmin(digits(k^2)), return(k^2)); k--) vector(20, n, a(n)) \\ Derek Orr, Mar 29 2015 CROSSREFS Cf. A104265, A104264, A052041. Sequence in context: A113361 A180737 A068881 * A061433 A069659 A271556 Adjacent sequences:  A104263 A104264 A104265 * A104267 A104268 A104269 KEYWORD nonn,base AUTHOR Reinhard Zumkeller, Feb 26 2005 EXTENSIONS More terms from Robert G. Wilson v, Mar 03 2005 More terms from Jon E. Schoenfield, Mar 29 2015 STATUS approved

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Last modified October 22 01:48 EDT 2021. Contains 348160 sequences. (Running on oeis4.)