A343075 - OEIS

%I #25 Apr 05 2021 04:01:54

%S 25,121,144,169,196,256,289,324,1024,1089,1156,1296,1369,1444,1521,

%T 1681,1764,1849,1936,2500,3136,3249,3364,3481,3721,3844,3969,4096,

%U 4356,4489,4624,4761,5041,5184,6084,6241,6561,6724,6889,7056,7396

%N Digitally delicate square numbers (changing any one decimal digit always produces a nonsquare).

%C If k is the count of digitally delicate square numbers <= n, then empirically lim_{n->oo} k/n = sqrt(5)/3.

%e 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.

%t 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 *)

%o (Python)

%o from sympy import integer_nthroot

%o def is_square(n): return integer_nthroot(n, 2)[1]

%o def change1(n):

%o   s = str(n)

%o   for i in range(len(s)):

%o     for d in set("0123456789") - {s[i]}:

%o       yield int(s[:i] + d + s[i+1:])

%o def ok(sqr): return not any(is_square(t) for t in change1(sqr))

%o print(list(filter(ok, (k*k for k in range(87))))) # _Michael S. Branicky_, Apr 04 2021

%Y Cf. A000290, A050249.

%K nonn,base

%O 1,1

%A _Ctibor O. Zizka_, Apr 04 2021