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A029793
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Numbers k such that k and k^2 have the same set of digits.
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17
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0, 1, 10, 100, 1000, 4762, 4832, 10000, 10376, 10493, 11205, 12385, 12650, 14829, 22450, 23506, 24605, 26394, 34196, 36215, 47620, 48302, 48320, 49827, 64510, 68474, 71205, 72510, 72576, 74510, 74528, 79286, 79603, 79836, 94583, 94867, 96123, 98376
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refs;
listen;
history;
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internal format)
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OFFSET
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1,3
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COMMENTS
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This sequence has density 1: almost all numbers k have all 10 digits in both k and k^2. - Franklin T. Adams-Watters, Jun 28 2011
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LINKS
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EXAMPLE
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{0, 1, 3, 4, 9} = digits of a(10) = 10493 and of 10493^2 = 110103049;
{0, 1, 2, 5, 6} = digits of a(100) = 162025 and of 162025^2 = 26252100625;
{0, 1, 3, 4, 6, 7, 8} = digits of a(1000) = 1764380 and of 1764380^2 = 3113036784400;
{1, 2, 3, 4, 7, 8, 9} = digits of a(10000) = 14872239 and of 14872239^2 = 221183492873121.
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MAPLE
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seq(`if`(convert(convert(n, base, 10), set) = convert(convert(n^2, base, 10), set), n, NULL), n=0..100000); # Nathaniel Johnston, Jun 28 2011
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MATHEMATICA
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digitSet[n_] := Union[IntegerDigits[n]]; Select[Range[0, 99000], digitSet[#] == digitSet[#^2] &] (* Jayanta Basu, Jun 02 2013 *)
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PROG
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(Haskell)
import Data.List (nub, sort)
a029793 n = a029793_list !! (n-1)
a029793_list = filter (\x -> digs x == digs (x^2)) [0..]
where digs = sort . nub . show
(Magma) [ n: n in [0..10^5] | Set(Intseq(n)) eq Set(Intseq(n^2)) ]; // Bruno Berselli, Jun 28 2011
(Scala) (0L to 99999L).filter(n => n.toString.toCharArray.toSet == (n * n).toString.toCharArray.toSet) // Alonso del Arte, Jan 19 2020
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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