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

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

Links

Table of n, a(n) for n=2..20.

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 A377591

Adjacent sequences: A287295 A287296 A287297 * A287299 A287300 A287301

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