(Translated by https://www.hiragana.jp/)
A287298 - OEIS
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A287298
a(n) is the largest square with distinct digits in base n.
1
1, 1, 225, 576, 38025, 751689, 10323369, 355624164, 9814072356, 279740499025, 8706730814089, 23132511879129, 11027486960232964, 435408094460869201, 18362780530794065025, 48470866291337805316, 39207739576969100808801, 1972312183619434816475625, 104566626183621314286288961
OFFSET
2,3
COMMENTS
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
EXAMPLE
a(4)=225 which is 3201 in base 4. Higher squares have at least 5 digits in base 4.
PROG
(Python)
from gmpy2 import isqrt, mpz, digits
def A287298(n): # assumes n <= 62
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)
return int(m2) # Chai Wah Wu, May 24 2017
CROSSREFS
Sequence in context: A147276 A219022 A193003 * A117246 A352518 A027470
KEYWORD
nonn,base
AUTHOR
John L. Drost, May 22 2017
EXTENSIONS
Added a(16)-a(20) and corrected a(12) by Chai Wah Wu, May 24 2017
STATUS
approved