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

%I A143691 #12 Apr 10 2018 14:38:41
%S A143691 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,
%T A143691 33,27,34,28,35,29,36,30,38,31,39,32,40,37,46,41,49,42,51,43,54,44,55,
%U A143691 45,56,47,57,48,58,50,60,52,62,53,64,59,65,61,69,63,74,66,77,67,81,68
%N A143691 Lexicographically earliest permutation of the natural numbers having alternating even and odd numbers of prime factors.
%C A143691 A066829(a(n)*a(n+1)) = 1; n mod 2 + A001222(a(n)) = 1;
%C A143691 a(2*n) = A026424(n); a(2*n-1) = A028260(n);
%C A143691 a(a(n)) = A143693(n).
%H A143691 Reinhard Zumkeller, <a href="/A143691/b143691.txt">Table of n, a(n) for n = 1..10000</a>
%H A143691 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o A143691 (Haskell)
%o A143691 import Data.List (delete)
%o A143691 a143691 n = a143691_list !! (n-1)
%o A143691 a143691_list = f 1 [1..] where
%o A143691    f m xs = g xs where
%o A143691      g (z:zs) = if m + m' /= 1 then g zs else z : f m' (delete z xs)
%o A143691                 where m' = a001222 z `mod` 2
%o A143691 -- _Reinhard Zumkeller_, Aug 07 2014
%Y A143691 Cf. A143692 (inverse), A001222, A066829, A026424, A028260, A143693, A109465.
%K A143691 nonn
%O A143691 1,2
%A A143691 _Reinhard Zumkeller_, Aug 29 2008