Magic constant: Difference between revisions

=={{header|Nim}}==

<syntaxhighlight lang="Nim">import std/[math, unicode]

func magicConstant(n: int): int =

## Return the magic constant for a magic square of order "n".

n * (n * n + 1) div 2

func minOrder(value: int): int =

## Return the smallest order such as the magic constant is greater than "value".

let start = int(cbrt(value.toFloat * 2))

result = start

while result.magicConstant < value:

inc result

const First = 3

const Superscripts: array['0'..'9', string] = ["⁰", "¹", "²", "³", "⁴", "⁵", "⁶", "⁷", "⁸", "⁹"]

template order(idx: Positive): int =

## Compute the order of the magic square at index "idx".

idx + (First - 1)

func superscript(n: Natural): string =

## Return the Unicode string to use to represent an exponent.

for d in $n:

result.add(Superscripts[d])

echo "First 20 magic constants:"

for idx in 1..20:

stdout.write ' ', order(idx).magicConstant

echo()

echo "\n1000th magic constant: ", order(1000).magicConstant

echo "\nOrder of the smallest magic square whose constant is greater than:"

for n in 1..18:

let left = "10" & n.superscript & ':'

echo left.alignLeft(6), ($minOrder(10^n)).align(7)

</syntaxhighlight>

{{out}}

For the stretch task, as integers are 64 bits long, we are limited to 10^18. To go further, we would have to use external libraries such as <code>bigints</code>, <code>bignum</code> or <code>integers</code>.

<pre>First 20 magic constants:

15 34 65 111 175 260 369 505 671 870 1105 1379 1695 2056 2465 2925 3439 4010 4641 5335

1000th magic constant: 503006505

Order of the smallest magic square whose constant is greater than:

10¹: 3

10²: 6

10³: 13

10⁴: 28

10⁵: 59

10⁶: 126

10⁷: 272

10⁸: 585

10⁹: 1260

10¹⁰: 2715

10¹¹: 5849

10¹²: 12600

10¹³: 27145

10¹⁴: 58481

10¹⁵: 125993

10¹⁶: 271442

10¹⁷: 584804

10¹⁸: 1259922

</pre>