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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.
4
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
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
KEYWORD
easy,nonn
AUTHOR
Christer Mauritz Blomqvist (MauritzTortoise(AT)hotmail.com), Apr 09 2004
STATUS
approved