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A132147 Numbers that are the sum of a prime number and a positive Fibonacci number. 4
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 (list; graph; refs; listen; history; text; internal format)
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,changed

AUTHOR

Tanya Khovanova, Aug 12 2007

STATUS

approved

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Last modified March 9 03:05 EST 2021. Contains 341961 sequences. (Running on oeis4.)