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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.

%I A092579 #5 Oct 06 2019 10:34:25
%S A092579 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,49,53,59,61,67,71,73,77,79,
%T A092579 83,89,97,101,103,107,109,113,119,121,127,131,133,137,139,149,151,157,
%U A092579 161,163,167,173,179,181,187,191,193,197,199,203,209,211,217,223,227,229
%N 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.
%C A092579 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.
%C A092579 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).
%H A092579 Amiram Eldar, <a href="/A092579/b092579.txt">Table of n, a(n) for n = 1..10000</a>
%e A092579 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.
%t A092579 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. *)
%Y A092579 Cf. A000045, A000040, A005478.
%K A092579 easy,nonn
%O A092579 1,1
%A A092579 Christer Mauritz Blomqvist (MauritzTortoise(AT)hotmail.com), Apr 09 2004