A132145 - OEIS

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

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OFFSET

1,1

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]

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.

EXAMPLE

11 = 3+8, the sum of a prime number (3) and a Fibonacci number (8).

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