A034289 Squares which can be rearranged into squares with the same number of digits.

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

Offset

1,1

Comments

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

There are 87 10-digit 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

B-file shortened by N. J. A. Sloane, Dec 08 2018

Status

approved