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

1,1

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

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).

Example

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

Mathematica

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

Prog

(PARI) is(n)=my(k, f); while((f=fibonacci(k++))<n, if(isprime(n-f), return(1))); 0 \\ Charles R Greathouse IV, Sep 14 2015

Crossrefs

Cf. A000040, A000045, A132145, A132146.

Sequence in context: A026505 A029674 A192452 * A118955 A191838 A333214

Adjacent sequences: A132144 A132145 A132146 * A132148 A132149 A132150

Keyword

nonn

Author

Tanya Khovanova, Aug 12 2007

Status

approved