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A359345 Roots of largest pandigital squares with n digits.

%I A359345 #8 Dec 31 2022 02:13:03
%S A359345 99066,315996,999366,3162039,9999629,31622524,99999629,316227746,
%T A359345 999999629,3162277591,9999999629,31622776461,99999999629,316227765995,
%U A359345 999999999629,3162277660155,9999999999629,31622776601681,99999999999629,316227766016811,999999999999629
%N A359345 Roots of largest pandigital squares with n digits.
%C A359345 Pandigital squares are perfect squares containing each digit from 0 to 9 at least once.
%F A359345 a(n) = sqrt(A359344(n)).
%F A359345 a(n) = (10^(n/2-3) - 1)*10^3 + 629 for n >= 14 even.
%o A359345 (Python)
%o A359345 from math import isqrt
%o A359345 def c(n): return len(set(str(n))) == 10
%o A359345 def a(n):
%o A359345     ub, lb = isqrt(10**n-1), isqrt(10**(n-1)) if n&1 else isqrt(10**(n-1))+1
%o A359345     return next((k for k in range(ub, lb-1, -1) if c(k*k)), None)
%o A359345 print([a(n) for n in range(10, 31)]) # _Michael S. Branicky_, Dec 27 2022
%Y A359345 Cf. A359343, A359344.
%K A359345 nonn,base
%O A359345 10,1
%A A359345 _Martin Renner_, Dec 27 2022