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 A029793 Numbers k such that k and k^2 have the same set of digits. 16
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 EXAMPLE {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. MAPLE 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 MATHEMATICA digitSet[n_] := Union[IntegerDigits[n]]; Select[Range[0, 99000], digitSet[#] == digitSet[#^2] &] (* Jayanta Basu, Jun 02 2013 *) PROG (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 -- Reinhard Zumkeller, Jun 27 2011 (MAGMA) [ n: n in [0..10^5] | Set(Intseq(n)) eq Set(Intseq(n^2)) ];  // Bruno Berselli, Jun 28 2011 (PARI) isA029793(n)=Set(Vec(Str(n)))==Set(Vec(Str(n^2))) \\ Charles R Greathouse IV, Jun 28 2011 (Scala) (0L to 99999L).filter(n => n.toString.toCharArray.toSet == (n * n).toString.toCharArray.toSet) // Alonso del Arte, Jan 19 2020 CROSSREFS Cf. A029795, A029797, A030091; A178501 is a subsequence, A054038, A171102, A232659-A232662. Sequence in context: A031201 A228989 A072083 * A233453 A136877 A257969 Adjacent sequences:  A029790 A029791 A029792 * A029794 A029795 A029796 KEYWORD nonn,base AUTHOR STATUS approved

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Last modified April 23 07:37 EDT 2021. Contains 343201 sequences. (Running on oeis4.)