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A054031
Numbers whose square contains exactly 3 distinct digits.
10
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
KEYWORD
nonn,base
AUTHOR
Asher Auel, Feb 29 2000
STATUS
approved