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

1,1

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.

Formula

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A048037 A346657 A171492 * A060275 A083984 A272022

Adjacent sequences: A054028 A054029 A054030 * A054032 A054033 A054034

Keyword

nonn,base

Author

Asher Auel, Feb 29 2000

Status

approved