A227113 Lexicographically earliest permutation of the natural numbers such that all pairs of even- and odd-indexed terms have a common divisor > 1.
1, 2, 4, 3, 6, 5, 10, 7, 14, 8, 12, 9, 15, 11, 22, 13, 26, 16, 18, 17, 34, 19, 38, 20, 24, 21, 27, 23, 46, 25, 30, 28, 32, 29, 58, 31, 62, 33, 36, 35, 40, 37, 74, 39, 42, 41, 82, 43, 86, 44, 48, 45, 50, 47, 94, 49, 56, 51, 54, 52, 60, 53, 106, 55, 65, 57, 63
Offset: 1
Keywords
Examples
. n | a(2n) a(2n+1) | GCD | not occurring after step n
. ---+---------------+-----+-------------------------------------------
. 0 | _ 1 | _ | {2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,..}
. 1 | 2 4 | 2 | {3,5,6,7,8,9,10,11,12,13,14,15,16,17,..}
. 2 | 3 6 | 3 | {5,7,8,9,10,11,12,13,14,15,16,17,18,19,..}
. 3 | 5 10 | 5 | {7,8,9,11,12,13,14,15,16,17,18,19,20,..}
. 4 | 7 14 | 7 | {8,9,11,12,13,15,16,17,18,19,20,21,22,..}
. 5 | 8 12 | 4 | {9,11,13,15,16,17,18,19,20,21,22,23,24..}
. 6 | 9 15 | 3 | {11,13,16,17,18,19,20,21,22,23,24,25,..}
. 7 | 11 22 | 11 | {13,16,17,18,19,20,21,23,24,25,26,27,..}
. 8 | 13 26 | 11 | {16,17,18,19,20,21,23,24,25,27,28,29,..}
. 9 | 16 18 | 2 | {17,19,20,21,23,24,25,27,28,29,30,31,..} .
Links
Programs
-
Haskell
import Data.List (delete) a227113 n = a227113_list !! (n-1) a227113_list = 1 : f [2..] where f (x:xs) = x : y : f (delete y xs) where y : _ = filter ((> 1) . (gcd x)) xs
Extensions
Thanks to Zak Seidov (who suggested more elaboration) from Reinhard Zumkeller, Jul 05 2013
Comments