A magic square is a square grid containing consecutive integers from 1 to N², arranged so that every row, column and diagonal adds up to the same number. That number is a constant. There is no way to create a valid N x N magic square that does not sum to the associated constant. 

;EG

A 3 x 3 magic square ''always'' sums to 15. 

<pre style="font-family: consolas, inconsolata, monospace; line-height: normal;">    ┌───┬───┬───┐
    │ 2 │ 7 │ 6 │
    ├───┼───┼───┤
    │ 9 │ 5 │ 1 │
    ├───┼───┼───┤
    │ 4 │ 3 │ 8 │
    └───┴───┴───┘</pre>

A 4 x 4 magic square ''always'' sums to 34.

Traditionally, the sequence leaves off terms for n = 0 and n = 1 as the magic squares of order 0 and 1 are trivial; and a term for n = 2 because it is impossible to form a magic square of order 2.


;Task

* Starting at order 3, show the first 20 magic constants.
* Show the 1000th magic constant. (Order 1003)
* Find and show the order of the smallest N x N magic square whose constant is greater than 10¹ through 10¹⁰.


;Stretch

* Find and show the order of the smallest N x N magic square whose constant is greater than 10¹¹ through 10²⁰.


;See also

* [[wp:Magic_constant|Wikipedia: Magic constant]]
* [[oeis:A006003|OEIS: A006003]] (Similar sequence, though it includes terms for 0, 1 & 2.)
* [[Magic squares of odd order]]
* [[Magic squares of singly even order]]
* [[Magic squares of doubly even order]]