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%I #19 Sep 03 2017 22:00:35
%S 4,9,8,15,6,25,10,21,14,27,12,35,16,33,22,39,18,49,20,51,26,45,24,55,
%T 28,57,32,65,30,77,34,63,38,69,36,85,40,75,44,81,42,95,46,87,52,91,48,
%U 115,50,93,56,99,54,119,58,111,62,105,60,121,64,117,68,123,66,125,70,129,74
%N a(n) = the smallest composite positive integer that is not yet in the sequence and that is coprime to n.
%C This sequence is a permutation of the composite positive integers.
%C Indices of composites: {1, 4, 3, 8, 2, 15, 5, 12, 7, 17, 6, 23, 9, 21, 13, 26, 10, 33, 11, 35, 16, 30, 14, 38, 18, 40, 20, 46, ...}. - _Michael De Vlieger_, Jul 23 2017
%C Each composite k occurs in the sequence no later than a(k-1). Proof by induction. - _Peter Munn_, Sep 01 2017
%H Michael De Vlieger, <a href="/A163642/b163642.txt">Table of n, a(n) for n = 1..3000</a>
%t a = {4}; Do[k = 6; While[Nand[CompositeQ@ k, ! MemberQ[a, k], CoprimeQ[k, n]], k++]; AppendTo[a, k], {n, 2, 69}]; a (* _Michael De Vlieger_, Jul 23 2017 *)
%Y Cf. A085084, A163643.
%K nonn,easy
%O 1,1
%A _Leroy Quet_, Aug 02 2009
%E More terms from _Sean A. Irvine_, Nov 11 2009
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