Any natural number can be written uniquely as a sum of nonconsecutive ones of these numbers by Zeckendorf's theorem. The worst-case runtime of the Euc
Any natural number can be written uniquely as a sum of nonconsecutive ones of these numbers by Zeckendorf's theorem. The worst-case runtime of the Euclidean algorithm is for a consecutive pair of these. Three of these numbers cannot form a Pythagorean triplet, and neither can the similar Lucas numbers. The ratio of each number to the previous one in this sequence approaches one plus the square root of five over two, or the golden ratio. For 10 points, give this sequence of numbers named after an Italian mathematician in which each term is the sum of the previous two terms, beginning one, one, two, three, five. 
Any natural number can be written uniquely as a sum of nonconsecutive ones of these numbers by Zeckendorf's theorem.
Fibonacci sequence [accept word forms] 