A029793 Numbers k such that k and k^2 have the same set of digits.

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

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 A358442 A136877

Adjacent sequences: A029790 A029791 A029792 * A029794 A029795 A029796

Keyword

nonn,base

Author

Patrick De Geest

Status

approved