Euler project: Ulam spiral

Spiral like this:

This spiral is famous because it has the fact that most of prime number are present on the diagonal position of this rectangular.

Euler problem ask for the sum of all diagonal numbers like red ones above. The prime feature could not be used because not all diagonal positions are prime number. The hint is just every turn in this spiral, the length goes like: 1, 1, 2, 2, 3, 3, 4, 4,...

Since every turn is also the diagonal, except the first one, 2, use this length growth to build the sum is easy:

	def approach1(size):
	diagonal = 0
	current = 1
	for i in range(1, size+1):
	current += i
	diagonal += current
	# decrease the sum if it is the first odd turn
	if i%2 != 0:
	diagonal -= 1
	current += i
	diagonal += current
	# remove the last turn
	diagonal -= current
	print diagonal

view raw gistfile1.py hosted with ❤ by GitHub

Every first odd turn should be taken care of because the actual diagonal number is the one before the turn number. Also, note the last turn is not included to form the required rectangular.