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The Collatz conjecture, named after Lothar Collatz who introduced the idea is a perfect example of a mathematical problem that cannot be solved by mathematics and the tools available within the domain and scope of mathematics of today.

It goes a little like this:

$${\displaystyle f(n)={\begin{cases}{\frac {n}{2}}&{\text{if }}n\equiv 0{\pmod {2}}\\[4px]3n+1&{\text{if }}n\equiv 1{\pmod {2}}.\end{cases}}}$$

it's a nice little conjecture to turn into a program, so I decided to write it in YASS to try and demonstrate this based on the above syntax:

YASS
function f ($n)

  if($n % 2 == 0)
    $n = $n / 2
  else
    $n = ($n * 3) + 1
  end if

  return $n

end function

$n = input("Please insert a start number")

$iterations = 0
print($n)
while($n != 0 and $iterations < 5)
  
  $n = f($n)

  print($n)
  if($n == 1)
    $iterations++
  end if
end while
Posted by J B Balfour in Tech talk