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A359343
Square roots of least pandigital squares with n digits.
2
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.
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
Sequence in context: A054038 A156977 A217368 * A097282 A264499 A249230
KEYWORD
nonn,base
AUTHOR
Martin Renner, Dec 27 2022
STATUS
approved