A104177 - OEIS

%I #7 Jun 23 2020 19:05:33

%S 1,3,7,9,15,19,21,31,33,37,39,45,51,61,63,67,69,75,79,81,93,97,99,109,

%T 111,121,123,127,129,135,139,141,151,157,165,169,171,181,183,189,195,

%U 199,201,211,213,219,225,229,231,241,243,247,249,255,261,271,277,279

%N A variation on Flavius's sieve (A000960): Start with the natural numbers; at the k-th sieving step, remove every f-th term of the sequence remaining after the (k-1)-st sieving step, where f is the (k+2)-nd Fibonacci number, f=F(k+2); iterate.

%C This sequence is approximately as dense as the lucky numbers or primes: there are 195 of these numbers, 153 lucky numbers and 168 primes less than 1000.

%H <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>

%e Start with

%e 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ... (A000027)

%e First sieving step: Delete every 2nd term (2=F(1+2)), giving

%e 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 ... (A005408)

%e 2nd sieving step: Delete every 3rd term (3=F(2+2)), giving

%e 1 3 7 9 13 15 19 21 25 27 31 ... (A056530)

%e 3rd sieving step: Delete every 5th (5=F(3+2)) term, giving

%e 1 3 7 9 15 19 21 25 31 ...

%e 4th sieving step: Delete every 8th (8=F(4+2)) term, giving

%e 1 3 7 9 15 19 21 31 ...

%e Continue forever and whatever remains is the sequence.

%Y Cf. A000960, A000959, A099204, A000045.

%K easy,nonn

%O 1,2

%A Tyler D. Rick (tyler.rick(AT)does.not.want.spam.com), Mar 11 2005