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

10,1

Comments

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

Links

Table of n, a(n) for n=10..30.

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

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

Prog

(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

Crossrefs

Cf. A359342, A359345.

Sequence in context: A054038 A156977 A217368 * A097282 A264499 A249230

Adjacent sequences: A359340 A359341 A359342 * A359344 A359345 A359346

Keyword

nonn,base

Author

Martin Renner, Dec 27 2022

Status

approved