An explicit formula generating the non-Fibonacci numbers

Publication date: 5 May 2011

Abstract: We show among others that the formula: $$ lfloor n + log_{Phi}{sqrt{5}(log_{Phi}(sqrt{5}n) + n) -5 + frac{3}{n}} - 2 floor (n geq 2), $$ (where $Phi$ denotes the golden ratio and $lfloor floor$ denotes the integer part) generates the non-Fibonacci numbers.

Has companion code repository: https://github.com/stdlib-js/math-iter-sequences-nonfibonacci

Mathematics Subject Classification ID

Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05)

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