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

0,2

Comments

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

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

Example

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,...

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 *)

Prog

(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

Crossrefs

Cf. A066680, A232054 (complement).

Sequence in context: A331916 A371127 A269390 * A308011 A087757 A188163

Adjacent sequences: A056872 A056873 A056874 * A056876 A056877 A056878

Keyword

nonn,easy,nice

Author

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

Status

approved