A287298 - OEIS

%I #11 May 24 2017 13:08:59

%S 1,1,225,576,38025,751689,10323369,355624164,9814072356,279740499025,

%T 8706730814089,23132511879129,11027486960232964,435408094460869201,

%U 18362780530794065025,48470866291337805316,39207739576969100808801,1972312183619434816475625,104566626183621314286288961

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

%C 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 a(22) = 340653564758245010607213613056. - _Chai Wah Wu_, May 24 2017

%e a(4)=225 which is 3201 in base 4. Higher squares have at least 5 digits in base 4.

%o (Python)

%o from gmpy2 import isqrt, mpz, digits

%o def A287298(n): # assumes n <= 62

%o     m = isqrt(mpz(''.join(digits(i,n) for i in range(n-1,-1,-1)),n))

%o     m2 = m**2

%o     d = digits(m2,n)

%o     while len(set(d)) < len(d):

%o         m -= 1

%o         m2 -= 2*m+1

%o         d = digits(m2,n)

%o     return int(m2) # _Chai Wah Wu_, May 24 2017

%K nonn,base

%O 2,3

%A _John L. Drost_, May 22 2017

%E Added a(16)-a(20) and corrected a(12) by _Chai Wah Wu_, May 24 2017