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A287298
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a(n) is the largest square with distinct digits in base n.
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1
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1, 1, 225, 576, 38025, 751689, 10323369, 355624164, 9814072356, 279740499025, 8706730814089, 23132511879129, 11027486960232964, 435408094460869201, 18362780530794065025, 48470866291337805316, 39207739576969100808801, 1972312183619434816475625, 104566626183621314286288961
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OFFSET
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2,3
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COMMENTS
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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.
a(22) = 340653564758245010607213613056. - Chai Wah Wu, May 24 2017
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LINKS
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EXAMPLE
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a(4)=225 which is 3201 in base 4. Higher squares have at least 5 digits in base 4.
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PROG
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(Python)
from gmpy2 import isqrt, mpz, digits
m = isqrt(mpz(''.join(digits(i, n) for i in range(n-1, -1, -1)), n))
m2 = m**2
d = digits(m2, n)
while len(set(d)) < len(d):
m -= 1
m2 -= 2*m+1
d = digits(m2, n)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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Added a(16)-a(20) and corrected a(12) by Chai Wah Wu, May 24 2017
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STATUS
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approved
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