A392242 Squares with distinct digits.

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 169, 196, 256, 289, 324, 361, 529, 576, 625, 729, 784, 841, 961, 1024, 1089, 1296, 1369, 1764, 1849, 1936, 2304, 2401, 2601, 2704, 2809, 2916, 3025, 3249, 3481, 3721, 4096, 4356, 4761, 5041, 5184, 5329, 5476, 6084, 6241, 6724, 7056

Offset

1,3

Comments

There are 611 terms, the largest being 99066^2 = 9814072356.

First differs from A052046 at a(54) = 7921 != 7444 = A052046(54).

First differs from A052062 at a(28) = 1764 != 1521 = A052062(28).

Links

Michael S. Branicky, Table of n, a(n) for n = 1..611

Formula

a(n) = A119509(n-1)^2. - R. J. Mathar, Jan 23 2026

Maple

q:= n-> (l-> nops(l)=nops({l[]}))(convert(n, base, 10)):
select(q, [i^2$i=0..84])[];  # Alois P. Heinz, Jan 18 2026

Mathematica

Join[{0}, Select[Range[0, 85]^2, CountDistinct[IntegerDigits[#]] == IntegerLength[#] &]] (* Stefano Spezia, Jan 18 2026 *)

Prog

(Python)
afull = [k**2 for k in range(10**5) if len(s:=str(k**2)) == len(set(s))]

Crossrefs

Complement of A392480 in A000290.

Subsequence of A078255.

Cf. A052046, A052062.

Sequence in context: A052062 A052046 A078255 * A077356 A077357 A294497

Adjacent sequences: A392239 A392240 A392241 * A392243 A392244 A392245

Keyword

nonn,base,easy,fini,full

Author

Michael S. Branicky, Jan 18 2026

Status

approved