A052041 Squares lacking the digit zero in their decimal expansion.

1, 4, 9, 16, 25, 36, 49, 64, 81, 121, 144, 169, 196, 225, 256, 289, 324, 361, 441, 484, 529, 576, 625, 676, 729, 784, 841, 961, 1156, 1225, 1296, 1369, 1444, 1521, 1681, 1764, 1849, 1936, 2116, 2916, 3136, 3249, 3364, 3481, 3721, 3844, 3969, 4225, 4356

Offset: 1

Author

Patrick De Geest, Dec 15 1999

Keywords

• nonn
• base

Comments

This sequence is infinite: see A075415 or A102807 for a constructive proof.

Intersection of A052382 and A000290; A168046(a(n))*A010052(a(n))=1. - Reinhard Zumkeller, Dec 01 2009

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Zerofree [From _Reinhard Zumkeller_, Dec 01 2009]

Crossrefs

Cf. A104264, A102265, A102266.

Squares: A052040, A052042, A052043. Cubes: A051750, A051751, A051832, A051833.

Programs

Mathematica

Select[Range[66]^2, FreeQ[IntegerDigits[#],0]==True &] (* Jayanta Basu, May 25 2013 *)

Formula

a(n) = A052040(n)^2. - R. J. Mathar, Jul 23 2025