A359343 Square roots of least pandigital squares with n digits.

32043, 100287, 317096, 1000287, 3162426, 10000287, 31622792, 100000287, 316227814, 1000000287, 3162277718, 10000000287, 31622776661, 100000000287, 316227766026, 1000000000287, 3162277660177, 10000000000287, 31622776601685, 100000000000287, 316227766016843

Offset: 10

Author

Martin Renner, Dec 27 2022

Keywords

• nonn
• base

Comments

Pandigital squares are perfect squares containing each digit from 0 to 9 at least once.

Crossrefs

Cf. A359342, A359345.

Programs

Maple

f:= proc(n); local k;
  for k from ceil(10^((n-1)/2)) do
    if convert(convert(k^2,base,10),set) = {$0..9} then return k fi
  od
end proc:
map(f, [$10..30]); # Robert Israel, Dec 29 2022

Python

from math import isqrt
def c(n): return len(set(str(n))) == 10
def a(n): return next((k for k in range(isqrt(10**(n-1))+1, isqrt(10**n-1)+1) if c(k*k)), None)
print([a(n) for n in range(10, 31)]) # Michael S. Branicky, Dec 27 2022

Formula

a(n) = sqrt(A359342(n)).

If n is odd, a(n) = 10^((n-1)/2) + 287. - Robert Israel, Dec 29 2022

a(n) = 10^((n-1)/2) + O(1). - Charles R Greathouse IV, Dec 30 2022