A132147 Numbers that are the sum of a prime number and a positive Fibonacci number.

3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76

Offset: 1

Author

Tanya Khovanova, Aug 12 2007

Keywords

• nonn

Comments

This sequence is a subsequence of A132145 and is the complement of A132146.

Lee shows that this sequence has positive lower density. - Charles R Greathouse IV, Nov 02 2010

The lower density of this sequence is at least 0.0254905 (Liu and Xue, 2021). - Amiram Eldar, Mar 04 2021

Examples

			11 = 3+8 is a term since it is the sum of a prime number (3) and a Fibonacci number (8).
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• K. S. Enoch Lee, On the sum of a prime and a Fibonacci number, International Journal of Number Theory, Vol. 6, No. 7 (2010), pp. 1669-1676; arXiv preprint, arXiv:1011.0173 [math.NT], 2010.
• Zhixin Liu and Mengyuan Xue, The sum of a prime and a Fibonacci number, International Journal of Number Theory (2021).

Crossrefs

Cf. A000040, A000045, A132145, A132146.

Programs

Mathematica

Take[Union[Flatten[Table[Fibonacci[n] + Prime[k], {n, 70}, {k, 70}]]], 70]

PARI

is(n)=my(k,f); while((f=fibonacci(k++))Charles R Greathouse IV, Sep 14 2015