The Smallest Positive Integer Having Fk Representations as Sums of Distinct Fibonacci Numbers

Marjorie Bicknell-Johnson

A chapter in Applications of Fibonacci Numbers, 1999, pp 47-52 from Springer

Abstract: Abstract Let R(N) be the number of representations of the nonnegative integer N as a sum of distinct Fibonacci numbers. Consider the specialized and related sequence 1, 3, 8, 16, 24, …, A n, whose nth term is the least positive integer N such that n = R(N). Fielder [3] has calculated {A n} for 1 ≤ n ≤ 330 and for 1 ≤ N ≤ F 28 - 1. This paper exhibits formulas for {A n} such that n = F k, L k, or 2F k.

Keywords: 11B39; 11B37; 11Y55 (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1007/978-94-011-4271-7_5

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