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

1,2

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

Prog

(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

Crossrefs

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

Sequence in context: A354453 A281120 A246682 * A129767 A119618 A113321

Adjacent sequences: A143688 A143689 A143690 * A143692 A143693 A143694

Keyword

nonn

Author

Reinhard Zumkeller, Aug 29 2008

Status

approved