A104177 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.

1, 3, 7, 9, 15, 19, 21, 31, 33, 37, 39, 45, 51, 61, 63, 67, 69, 75, 79, 81, 93, 97, 99, 109, 111, 121, 123, 127, 129, 135, 139, 141, 151, 157, 165, 169, 171, 181, 183, 189, 195, 199, 201, 211, 213, 219, 225, 229, 231, 241, 243, 247, 249, 255, 261, 271, 277, 279

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..58.

Index entries for sequences related to the Josephus Problem

Example

Start with
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ... (A000027)
First sieving step: Delete every 2nd term (2=F(1+2)), giving
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 ... (A005408)
2nd sieving step: Delete every 3rd term (3=F(2+2)), giving
1 3 7 9 13 15 19 21 25 27 31 ... (A056530)
3rd sieving step: Delete every 5th (5=F(3+2)) term, giving
1 3 7 9 15 19 21 25 31 ...
4th sieving step: Delete every 8th (8=F(4+2)) term, giving
1 3 7 9 15 19 21 31 ...
Continue forever and whatever remains is the sequence.

Crossrefs

Cf. A000960, A000959, A099204, A000045.

Sequence in context: A119681 A197625 A190811 * A099204 A219608 A070993

Adjacent sequences: A104174 A104175 A104176 * A104178 A104179 A104180

Keyword

easy,nonn

Author

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

Status

approved