A099204 A variation on Flavius's sieve (A000960): Start with the natural numbers; at the k-th sieving step, remove every p-th term of the sequence remaining after the (k-1)-st sieving step, where p is the k-th prime; iterate.

1, 3, 7, 9, 15, 19, 25, 31, 33, 37, 45, 51, 61, 63, 67, 69, 81, 85, 97, 105, 109, 111, 123, 129, 135, 141, 145, 151, 159, 169, 183, 189, 195, 201, 211, 213, 219, 225, 229, 241, 261, 265, 273, 277, 289, 291, 307, 315, 319, 321, 325, 339, 351, 355, 361, 375, 381

Offset: 1

Author

N. J. A. Sloane, Nov 16 2004

Keywords

• nonn
• easy

Examples

			Start with
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ... and delete every second term, giving
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 ... and delete every 3rd term, giving
1 3 7 9 13 15 19 21 25 27 ... and delete every 5th term, giving
1 3 7 9 15 19 21 25 ... and delete every 7th term, giving
.... Continue forever and what's left is the sequence.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..10000
• Index entries for sequences generated by sieves

Crossrefs

Cf. A000960, A099207, A099243.

Programs

Maple

S[1]:={seq(i,i=1..390)}: for n from 2 to 390 do S[n]:=S[n-1] minus {seq(S[n-1][ithprime(n-1)*i],i=1..nops(S[n-1])/ithprime(n-1))} od: S[390]; # Emeric Deutsch, Nov 17 2004

Mathematica

Clear[l,ps];ps=Prime[Range[100]];l=Range[400];Do[l=Drop[l,{First[ps],-1, First[ps]}];ps=Rest[ps],{17}];l (* Harvey P. Dale, Sep 03 2011 *)

Python

import sympy
from sympy import prime
def a(n):
  x = 1
  lst = []
  lst.extend(range(1, 1000))
  while x <= n:
    lst1 = []
    for i in lst:
      if (lst.index(i)+1)%prime(x)!=0:
        lst1.append(i)
    lst.clear()
    lst.extend(lst1)
    x += 1
  return lst1[n-1]
n = 1
while n < 100:
  print(a(n), end=', ')
  n += 1
# Derek Orr, Jun 16 2014

Extensions

More terms from Ray Chandler, Nov 16 2004