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A029793
Numbers k such that k and k^2 have the same set of digits.
17
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
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
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
Sequence in context: A031201 A228989 A072083 * A233453 A358442 A136877
KEYWORD
nonn,base
STATUS
approved