Euler 65

gistfile1.txt

# pattern in convergents of e
# 1 + 2 * 1 = 3
# 2 + 3 * 2 = 8
# 3 + 8 * 1 = 11
# new term = two terms ago + one term ago * i

def make_e(n):
	CF = [2]
	c = 1
	while len(CF)<n:
		CF = CF + [1,2*c,1]
		c += 1
	return CF
	
nlist = make_e(100)
start = [2,3]
for i in range (2,100):
	newterm = start[i-2] + start[i-1]*nlist[i]
	start.append(newterm)
	print i+1,newterm

sum = 0
for j in range (0,len(str(newterm))):
	digit = str(newterm)[j:j+1]
	sum = sum+int(digit)
print sum