A143691 Lexicographically earliest permutation of the natural numbers having alternating even and odd numbers of prime factors.

1, 2, 4, 3, 6, 5, 9, 7, 10, 8, 14, 11, 15, 12, 16, 13, 21, 17, 22, 18, 24, 19, 25, 20, 26, 23, 33, 27, 34, 28, 35, 29, 36, 30, 38, 31, 39, 32, 40, 37, 46, 41, 49, 42, 51, 43, 54, 44, 55, 45, 56, 47, 57, 48, 58, 50, 60, 52, 62, 53, 64, 59, 65, 61, 69, 63, 74, 66, 77, 67, 81, 68

Offset: 1

Author

Reinhard Zumkeller, Aug 29 2008

Keywords

• nonn

Comments

A066829(a(n)*a(n+1)) = 1; n mod 2 + A001222(a(n)) = 1;

a(2*n) = A026424(n); a(2*n-1) = A028260(n);

a(a(n)) = A143693(n).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A143692 (inverse), A001222, A066829, A026424, A028260, A143693, A109465.

Programs

Haskell

import Data.List (delete)
a143691 n = a143691_list !! (n-1)
a143691_list = f 1 [1..] where
   f m xs = g xs where
     g (z:zs) = if m + m' /= 1 then g zs else z : f m' (delete z xs)
                where m' = a001222 z `mod` 2
-- Reinhard Zumkeller, Aug 07 2014