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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). 3
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 (list; graph; refs; listen; history; text; internal format)
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
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
Take[Union[Flatten[Table[Fibonacci[n] + Prime[k], {n, 70}, {k, 70}]], Table[Prime[k], {k, 70}]], 70]
CROSSREFS
Sequence in context: A044922 A346447 A273883 * A272284 A322554 A330232
KEYWORD
nonn
AUTHOR
Tanya Khovanova, Aug 12 2007
STATUS
approved

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Last modified June 14 21:35 EDT 2024. Contains 373401 sequences. (Running on oeis4.)