Every integer can be represented as a unique sum of one or more distinct, nonconsecutive numbers in this series, according to Zeckendorf's theorem. An integer x is in this series if one or both of "five x squared plus four" or "five x squared minus four" is a perfect square, a consequence of Binet's formula. The shallow diagonals in Pascal's triangle sum to these numbers, which were used by their namesake to describe the population of a group of rabbits. As this series gets larger, the ratio of consecutive numbers in this series approaches the golden ratio. For 10 points, name this set of numb
Every integer can be represented as a unique sum of one or more distinct, nonconsecutive numbers in this series, according to Zeckendorf's theorem. An integer x is in this series if one or both of "five x squared plus four" or "five x squared minus four" is a perfect square, a consequence of Binet's formula. The shallow diagonals in Pascal's triangle sum to these numbers, which were used by their namesake to describe the population of a group of rabbits. As this series gets larger, the ratio of consecutive numbers in this series approaches the golden ratio. For 10 points, name this set of numbers with terms generated by adding the two preceding numbers, which begins 1, 1, 2, 3, 5.
Every integer can be represented as a unique sum of one or more distinct, nonconsecutive numbers in this series, according to Zeckendorf's theorem.