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A287298 a(n) is the largest square with distinct digits in base n.

%I A287298 #11 May 24 2017 13:08:59
%S A287298 1,1,225,576,38025,751689,10323369,355624164,9814072356,279740499025,
%T A287298 8706730814089,23132511879129,11027486960232964,435408094460869201,
%U A287298 18362780530794065025,48470866291337805316,39207739576969100808801,1972312183619434816475625,104566626183621314286288961
%N A287298 a(n) is the largest square with distinct digits in base n.
%C A287298 a(n) does not always have n digits in base n. If n is 5 mod 8 then a number which contains all the digits in base n is congruent to (n-1)n/2 mod (n-1). It will be then divisible by a single power of 2 and not a square.
%C A287298 a(22) = 340653564758245010607213613056. - _Chai Wah Wu_, May 24 2017
%e A287298 a(4)=225 which is 3201 in base 4. Higher squares have at least 5 digits in base 4.
%o A287298 (Python)
%o A287298 from gmpy2 import isqrt, mpz, digits
%o A287298 def A287298(n): # assumes n <= 62
%o A287298     m = isqrt(mpz(''.join(digits(i,n) for i in range(n-1,-1,-1)),n))
%o A287298     m2 = m**2
%o A287298     d = digits(m2,n)
%o A287298     while len(set(d)) < len(d):
%o A287298         m -= 1
%o A287298         m2 -= 2*m+1
%o A287298         d = digits(m2,n)
%o A287298     return int(m2) # _Chai Wah Wu_, May 24 2017
%K A287298 nonn,base
%O A287298 2,3
%A A287298 _John L. Drost_, May 22 2017
%E A287298 Added a(16)-a(20) and corrected a(12) by _Chai Wah Wu_, May 24 2017