A092579 A sieve using the Fibonacci sequence over the integers >=2. Any multiple of a Fibonacci number, F(n)*m, such that F(n)>=2 and m>=2 is excluded and what is left is included.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 77, 79, 83, 89, 97, 101, 103, 107, 109, 113, 119, 121, 127, 131, 133, 137, 139, 149, 151, 157, 161, 163, 167, 173, 179, 181, 187, 191, 193, 197, 199, 203, 209, 211, 217, 223, 227, 229

Offset

1,1

Comments

The first number in this sequence that differs from the sequence of primes is 49. This sequence will include more and more nonprime numbers since the density of this sequence nearly linear with just a bit below one number in four included in the sequence.

The density of numbers in the sequence will approach 1/4.129112110113143678897 = The limit of the product of the terms (1-1/pf(n)) as n goes from 1 to infinity and pf(n) is the prime Fibonacci numbers (A005478).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

The number 23 is included since it is not of the form F(n)*m, F(n)>=2, m>=2. The number 21 is excluded since 21=F(4)*7=3*7.

Mathematica

fs[s_] := (t = Floor[s/2]; v = Range[s]; f1 = 1; f2 = 1; While[f2 < t, f = f1 + f2; f1 = f2; f2 = f; n = 2*f2; While[n <= s, v[[n]] = 0; n = n + f2]]; Select[v, #>1 &]) (* This will generate all numbers in the sequence <=s. *)

Crossrefs

Cf. A000045, A000040, A005478.

Sequence in context: A249825 A117095 A054403 * A171028 A005180 A118848

Adjacent sequences: A092576 A092577 A092578 * A092580 A092581 A092582

Keyword

easy,nonn

Author

Christer Mauritz Blomqvist (MauritzTortoise(AT)hotmail.com), Apr 09 2004

Status

approved