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PROG
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(PARI) for(b=2, 12, for(k=1, oo, my(s=k^2, v=digits(s, b)); if(sum(k=1, #v, v[k]==0)==b, print1(k, ", "); break)))
(Python)
from numba import njit
@njit # works with 64 bits through a(14)
def digits0(n, b):
count0 = 0
while n >= b:
n, r = divmod(n, b)
count0 += (r==0)
return count0 + (n==0)
from sympy import integer_nthroot
def a(n):
an = integer_nthroot(n**n, 2)[0]
while digits0(an*an, n) != n: an += 1
return an
(Python)
from itertools import product
from functools import reduce
from sympy.utilities.iterables import multiset_permutations
from sympy import integer_nthroot
for a in range(1, n):
p, q = integer_nthroot(a*n**n, 2)
if q: return p
l = 1
while True:
cmax = n**(l+n+1)
for a in range(1, n):
c = cmax
for b in product(range(1, n), repeat=l):
for d in multiset_permutations((0, )*n+b):
p, q = integer_nthroot(reduce(lambda c, y: c*n+y, [a]+d), 2)
if q: c = min(c, p)
if c < cmax:
return c
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