A034289 - OEIS

%I #32 Dec 08 2018 13:54:10

%S 144,169,196,256,441,625,961,1024,1089,1296,1369,1764,1936,2401,2916,

%T 4096,4761,9216,9604,9801,10201,10404,10609,11236,11664,12100,12544,

%U 12769,14400,14884,16384,16641,16900,17689,18225,18769,19600,20736

%N Squares which can be rearranged into squares with the same number of digits.

%C Squares that have some nontrivial permutation of digits which are also squares.

%C There are 87 10-digit squares whose digits are a permutation of the digits 0..9. - _T. D. Noe_, Jan 23 2008

%H Gauray Kumar, <a href="/A034289/b034289.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1611 from T. D. Noe)

%H Gauray Kumar, <a href="/A034289/a034289.txt">Terms up to 10^9</a>

%e 144 is a square and so is 441, which is formed by rearranging the digits of 144.

%t sndQ[n_]:=Module[{p=Select[FromDigits/@Permutations[IntegerDigits[n]], IntegerLength[ #] == IntegerLength[n]&]},Length[Select[ p,IntegerQ[ Sqrt[#]]&]]>1]; Select[Range[150]^2,sndQ] (* _Harvey P. Dale_, Feb 18 2015 *)

%o (Perl)

%o #!/usr/bin/perl

%o # change this to compute more terms:

%o $max_digits = 5;

%o # put the squares into a hash table; for example

%o # 46 -> 64

%o # 144 -> 144 441

%o # 169 -> 169 196 961

%o $max_i = sqrt(10 ** $max_digits);

%o for $i (1..$max_i)

%o {

%o     $i_sq = $i * $i;

%o     $normalized = join('', sort(split(//, "$i_sq")));

%o     $sq_hash{"$normalized"} .= "$i_sq ";

%o }

%o # find the hash entries with more than one square

%o foreach (values(%sq_hash)) { $nums .= $_ if (/ \d/); }

%o # print the numbers in order

%o print join(' ', sort( { $a <=> $b } split(' ',"$nums")));

%o # Jonathan Cross (jcross(AT)juggler.net), Oct 18 2003

%K nonn,base

%O 1,1

%A _Erich Friedman_

%E B-file shortened by _N. J. A. Sloane_, Dec 08 2018