OFFSET
1,1
COMMENTS
If k is the count of digitally delicate square numbers <= n, then empirically lim_{n->oo} k/n = sqrt(5)/3.
EXAMPLE
n = 25, changing the digit 2 in 25 to d5, d from {0,1,3,4,5,6,7,8,9} gives no square, changing the digit 5 in 25 to 2d, d from {0,1,2,3,4,6,7,8,9} gives no square. Thus n = 25 is a member of the sequence.
MATHEMATICA
changes[n_] := Module[{d = IntegerDigits[n]}, FromDigits @ ReplacePart[d, First[#] -> Last[#]] & /@ Tuples[{Range[Length[d]], Range[0, 9]}]]; q[n_] := AllTrue[changes[n], # == n || ! IntegerQ @ Sqrt[#] &]; Select[Range[100]^2, q] (* Amiram Eldar, Apr 04 2021 *)
PROG
(Python)
from sympy import integer_nthroot
def is_square(n): return integer_nthroot(n, 2)[1]
def change1(n):
s = str(n)
for i in range(len(s)):
for d in set("0123456789") - {s[i]}:
yield int(s[:i] + d + s[i+1:])
def ok(sqr): return not any(is_square(t) for t in change1(sqr))
print(list(filter(ok, (k*k for k in range(87))))) # Michael S. Branicky, Apr 04 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Ctibor O. Zizka, Apr 04 2021
STATUS
approved