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 A343075 Digitally delicate square numbers (changing any one decimal digit always produces a nonsquare). 0
 25, 121, 144, 169, 196, 256, 289, 324, 1024, 1089, 1156, 1296, 1369, 1444, 1521, 1681, 1764, 1849, 1936, 2500, 3136, 3249, 3364, 3481, 3721, 3844, 3969, 4096, 4356, 4489, 4624, 4761, 5041, 5184, 6084, 6241, 6561, 6724, 6889, 7056, 7396 (list; graph; refs; listen; history; text; internal format)
 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. LINKS Table of n, a(n) for n=1..41. 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 Cf. A000290, A050249. Sequence in context: A206472 A036057 A083509 * A339130 A256519 A298009 Adjacent sequences: A343072 A343073 A343074 * A343076 A343077 A343078 KEYWORD nonn,base AUTHOR Ctibor O. Zizka, Apr 04 2021 STATUS approved

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Last modified November 30 23:40 EST 2023. Contains 367464 sequences. (Running on oeis4.)