14 sticks

I was cleaning up my attic recently and found a set of at least 14 sticks which a curious Italian sold me some years ago. Trying hard to figure out why I bought it from him, I realized that the set has the incredible property that there are no three sticks that can form a triangle. If the set has two sticks of length 1, which are the smallest, what is the least possible length of the 14th stick?

Correct answer:

x14 =  377

Step-by-step explanation:

x1=1 x2=1 x3=x1+x2=1+1=2 x4=x3+x2=2+1=3 x5=x4+x3=3+2=5 x6=x5+x4=5+3=8 x7=x6+x5=8+5=13 x8=x7+x6=13+8=21 x9=x8+x7=21+13=34 x10=x9+x8=34+21=55 x11=x10+x9=55+34=89 x12=x11+x10=89+55=144 x13=x12+x11=144+89=233 x14=x13+x12=233+144=377

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