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.
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Problem Comments
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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.
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