A242535 Start with the natural numbers and repeatedly take and keep the current initial term i, and remove m and 2m, where m = i-th term of the rest; repeat.

1, 3, 5, 6, 8, 9, 10, 12, 13, 16, 17, 18, 20, 21, 24, 25, 27, 28, 29, 32, 33, 35, 36, 37, 39, 41, 42, 44, 45, 48, 49, 50, 53, 54, 56, 57, 58, 59, 61, 63, 65, 66, 67, 70, 71, 73, 74, 76, 77, 78, 79, 82, 83, 85, 87, 88, 90, 91, 93, 95, 97, 98, 99, 101, 103

Offset: 1

Author

Reinhard Zumkeller, May 17 2014

Keywords

• nonn

Examples

			Start with 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,...
step 1: take 1, remove (1st term from the rest) = 2 and 2*2 = 4,
leaving 3,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26...
step 2: take 3, remove (3rd term from the rest) = 7 and 2*7 = 14,
leaving 5,6,8,9,10,11,12,13,15,16,17,18,19,20,21,22,23,24,25,26,27,28,...
step 3: take 5, remove (5th term from the rest) = 11 and 2*11 = 22,
leaving 6,8,9,10,12,13,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,...
step 4: take 6, remove (6th term from the rest) = 15 and 2*15 = 30,
leaving 8,9,10,12,13,16,17,18,19,20,21,23,24,25,26,27,28,29,31,32,33,...
step 5: take 8, remove (8th term from the rest) = 19 and 2*19 = 38,
leaving 9,10,12,13,16,17,18,20,21,23,24,25,26,27,28,29,31,32,33,34,35,...
step 6: take 9, remove (9th term from the rest) = 23, and 2*23 = 46,
leaving 10,12,13,16,17,18,20,21,24,25,26,27,28,29,31,32,33,34,35,36,...
		

Links

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

Crossrefs

Cf. A136119.

Programs

Haskell

import Data.List ((\\))
a242535 n = a242535_list !! (n-1)
a242535_list = f [1..] where
   f xs'@(x:xs) = x : f (xs \\ [z, 2 * z]) where z = xs' !! x