# On the sum of a prime and a Fibonacci number

@article{Lee2010OnTS, title={On the sum of a prime and a Fibonacci number}, author={K. S. Enoch Lee}, journal={arXiv: Number Theory}, year={2010} }

We show that the set of the numbers that are the sum of a prime and a Fibonacci number has positive lower asymptotic density.

## 8 Citations

On Numbers of the Form P + 2

- Mathematics
- 2014

Here, we show that the set of positive integers of the form p+2n−n where p is prime has a positive lower asymptotic density, thus answering a question of Z.-W. Sun. 2010 Mathematics Subject…

On integers not of the form Fn ± pa

- Mathematics
- 2016

In this paper, we prove a conjecture of Sun concerning the arithmetic progression of integers which contains no integers of the form Fn + p. In fact, we show that d − Fn has at least two distinct…

On the sumset of the primes and a linear recurrence

- Mathematics
- 2013

where en(F ) is the period of maximal length of the Fibonacci sequence modulo p as p varies through the prime divisors of n. In Lee’s work properties that may seem specific to the Fibonacci sequence…

Sums of primes and quadratic linear recurrence sequences

- Mathematics
- 2013

Let U be a sequence of positive integers which grows essentially as a geometric progression. We give a criterion on U in terms of its distribution modulo d, d = 1, 2, …, under which the set of…

Romanov type problems

- MathematicsThe Ramanujan journal
- 2018

Romanov proved that the proportion of positive integers which can be represented as a sum of a prime and a power of 2 is positive. We establish similar results for integers of the form…

The density of numbersnhaving a prescribed G.C.D. with thenth Fibonacci number

- MathematicsIndagationes Mathematicae
- 2018

The moments of the logarithm of a G.C.D. related to Lucas sequences

- MathematicsJournal of Number Theory
- 2018

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