A132145 Numbers that can be presented as a sum of a prime number and a Fibonacci number (0 is considered to be a Fibonacci number).

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 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, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72

Offset: 1

Author

Tanya Khovanova, Aug 12 2007

Keywords

• nonn

Comments

This sequence is the union of prime numbers and sequence A132147. It is also the complement of A132144.

Lee shows that the set of the numbers that are the sum of a prime and a Fibonacci number has positive lower asymptotic density. [Jonathan Vos Post, Nov 02 2010]

Examples

			11 = 3+8, 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, arXiv:1011.0173 [math.NT], 2010.

Crossrefs

Cf. A132144, A132147.

Programs

Maple

N:= 1000: # for all entries <= N
Primes:= select(isprime,{$1..N}):
phi:= (1+sqrt(5))/2:
Fibs:= {seq(combinat:-fibonacci(i),i=0..floor(log[phi]((N+1)*sqrt(5))))}:
sort(convert(select(`<=`,{seq(seq(f+p,f=Fibs),p=Primes)},N),list)); # Robert Israel, Aug 03 2015

Mathematica

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