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A029793
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Numbers n such that n and n^2 have the same set of digits.
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5
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| This sequence has density 1: almost all numbers n have all 10 digits in both n and n^2. - Franklin T. Adams-Watters, Jun 28 2011
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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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.
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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
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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
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CROSSREFS
| Cf. A029795, A029797, A030091; A178501 is a subsequence, A054038, A171102.
Sequence in context: A136863 A031201 A072083 * A136877 A125904 A190016
Adjacent sequences: A029790 A029791 A029792 * A029794 A029795 A029796
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KEYWORD
| nonn,base
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AUTHOR
| Patrick De Geest (pdg(AT)worldofnumbers.com)
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