A056875 Generated by sieving the natural numbers: keep the smallest remaining number k and take out its k-th successor l as well as the l-th successor m of l, the m-th successor of m and so on. Then start again from the next remaining number.

1, 3, 5, 6, 9, 10, 11, 13, 14, 18, 19, 20, 21, 23, 24, 27, 28, 30, 33, 34, 36, 38, 40, 41, 42, 43, 44, 46, 47, 50, 51, 53, 55, 58, 59, 60, 62, 65, 68, 69, 70, 71, 73, 74, 76, 79, 80, 82, 83, 84, 85, 88, 89, 91, 92, 93, 95, 96, 97, 101, 102, 103, 105, 106, 109, 111, 113, 114

Offset: 0

Author

Thomas Schulze (jazariel(AT)tiscalenet.it), Sep 02 2000

Keywords

• nonn
• easy
• nice

Comments

These numbers are homogeneously distributed with a density of approximately 0.59060.

Examples

			In the first round one starts with 1 and the numbers 2,4,8,16,... are removed leaving 1,3,5,6,7,9,10,11,12,13,14,15,17,18,19,20,... The third successor of 3 is now 7 and the 7th of 7 is 15 leaving 1,3,5,6,8,9,10,11,12,13,14,16,...
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Sieve
• Wikipedia, Sieve theory
• Index entries for sequences generated by sieves

Crossrefs

Cf. A066680, A232054 (complement).

Programs

Haskell

a056875 n = a056875_list !! (n-1)
a056875_list =  f [1..] where
   f zs = head zs : f (g zs) where
     g (x:xs) = us ++ g vs where (us, vs) = splitAt (x - 1) xs
-- Reinhard Zumkeller, Sep 11 2013

Mathematica

S = Range[200]; S0 = {}; i = 1;
While[S != S0, ii = NestWhileList[#+S[[#]] &, i+S[[i]], # <= Length[S]&]; S0 = S; S = Delete[S, List /@ Select[ii, # <= Length[S]&]]; i++];
S (* Jean-François Alcover, Dec 11 2019 *)