A054031 Numbers whose square contains exactly 3 distinct digits.

13, 14, 16, 17, 18, 19, 23, 24, 25, 27, 28, 29, 31, 34, 35, 39, 40, 41, 45, 46, 47, 50, 56, 58, 60, 62, 63, 65, 67, 68, 70, 75, 76, 77, 80, 81, 83, 85, 90, 91, 92, 94, 97, 101, 102, 107, 108, 110, 111, 119, 120, 121, 122, 129, 131, 141, 149, 150, 162, 165

Offset: 1

Author

Asher Auel, Feb 29 2000

Keywords

• nonn
• base

Links

• Giovanni Resta, Table of n, a(n) for n = 1..12299 (terms < 10^18, first 1000 terms from T. D. Noe)
• Michael Geißer, Theresa Körner, Sascha Kurz, and Anne Zahn, Squares with three digits, arXiv:2112.00444 [math.NT], 2021-2022.
• Carlos Rivera, Puzzle 313. Squares having only k distinct digits, The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A235718, A016069, A054032, A054033, A054034, A054035, A054036, A054037, A054038, A054039.

Programs

Maple

f := []; for i from 0 to 200 do if nops({op(convert(i^2,base,10))})=3 then f := [op(f),i] fi; od; f;

Mathematica

t = {}; n = -1; While[Length[t] < 50, n++; If[Length[Union[IntegerDigits[n^2]]] == 3, AppendTo[t, n]]] (* T. D. Noe, Apr 26 2013 *)
Select[Range[200],Length[Union[IntegerDigits[#^2]]]==3&] (* Harvey P. Dale, Aug 17 2014 *)

PARI

is(n)=#Set(digits(n^2))==3 \\ Charles R Greathouse IV, Feb 11 2017

Formula

A235718(n) = a(n)^2. - Giovanni Resta, Apr 28 2017