

A034289


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


4



144, 169, 196, 256, 441, 625, 961, 1024, 1089, 1296, 1369, 1764, 1936, 2401, 2916, 4096, 4761, 9216, 9604, 9801, 10201, 10404, 10609, 11236, 11664, 12100, 12544, 12769, 14400, 14884, 16384, 16641, 16900, 17689, 18225, 18769, 19600, 20736
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OFFSET

1,1


COMMENTS

Squares that have some nontrivial permutation of digits which are also squares.
There are 87 10digit squares whose digits are a permutation of the digits 0..9.  T. D. Noe, Jan 23 2008


LINKS

Gauray Kumar, Table of n, a(n) for n = 1..10000 (terms 1..1611 from T. D. Noe)
Gauray Kumar, Terms up to 10^9


EXAMPLE

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


MATHEMATICA

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 *)


PROG

(Perl)
#!/usr/bin/perl
# change this to compute more terms:
$max_digits = 5;
# put the squares into a hash table; for example
# 46 > 64
# 144 > 144 441
# 169 > 169 196 961
$max_i = sqrt(10 ** $max_digits);
for $i (1..$max_i)
{
$i_sq = $i * $i;
$normalized = join('', sort(split(//, "$i_sq")));
$sq_hash{"$normalized"} .= "$i_sq ";
}
# find the hash entries with more than one square
foreach (values(%sq_hash)) { $nums .= $_ if (/ \d/); }
# print the numbers in order
print join(' ', sort( { $a <=> $b } split(' ', "$nums")));
# Jonathan Cross (jcross(AT)juggler.net), Oct 18 2003


CROSSREFS

Sequence in context: A294575 A205190 A085426 * A062917 A035090 A064021
Adjacent sequences: A034286 A034287 A034288 * A034290 A034291 A034292


KEYWORD

nonn,base


AUTHOR

Erich Friedman


EXTENSIONS

Bfile shortened by N. J. A. Sloane, Dec 08 2018


STATUS

approved



