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
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