Problem 47073. Find the nth Fibbinary number
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.
Solution Stats
Problem Comments
-
2 Comments
Nikolaos Nikolaou
on 25 Oct 2020
Its a nice series of problems and i think there are more than enough untied problems for another Sequence and Series problem group. So maybe Chris its about time to curate one :)
ChrisR
on 25 Oct 2020
Thanks Nikolaos. I was thinking of making a group on primes, but one on sequences and series is a good idea.
Solution Comments
Show commentsProblem Recent Solvers11
Suggested Problems
-
Find the longest sequence of 1's in a binary sequence.
6194 Solvers
-
7640 Solvers
-
21189 Solvers
-
Make a run-length companion vector
638 Solvers
-
95 Solvers
More from this Author275
Problem Tags
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!