Problem 47073. Find the nth Fibbinary number

• Created by ChrisR
• Appears in Cody Problems in Japanese

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The numbers 0, 1, 2, 4, 5, 8, 9, and 10 form the first eight elements (i.e., elements to ) of the Fibbinary sequence. The name is a portmanteau that arose because of connections to Fibonacci numbers and binary numbers. The connection to Fibonacci numbers is that if the Zeckendorf expansion of n is

,

then

The connection to binary numbers is that the binary representations of the Fibbinary numbers have no adjacent 1s.

For example, = 10. The Zeckendorf expansion of 7 is 2+5, or , and

Also, the binary expansion of 10 is 1010, which has no adjacent 1s.

Write a function to find the nth Fibbinary number.

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Solution Stats

35.14% Correct | 64.86% Incorrect

• 37 Solutions
• 11 Solvers

Last Solution submitted on May 11, 2023

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