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%I #9 Feb 17 2015 14:56:44
%S 1,2,4,3,6,5,10,7,14,9,12,11,22,13,26,15,18,17,34,19,38,21,24,23,46,
%T 25,20,27,30,29,58,31,62,33,36,35,28,37,74,39,42,41,82,43,86,45,40,47,
%U 94,49,56,51,48,53,106,55,44,57,54,59,118,61,122,63,60,67
%N Beginning with 1, (a(2n-1),a(2n)) = 1, (a(2n),a(2n+1))>1; a(n) is smallest value not yet used that makes this true.
%C It seems that for n>1, a(2n-1) is always even, which forces a(2n) to be odd. Together, these prevent any further powers of 2 from appearing in the sequence. In fact, it appears that a(2n+1) is always either less than a(2n) or equal to a(2n) + the least prime factor of a(2n); and very rarely is a(2n) anything other than the smallest odd number not yet used (the first instance for n>1 is a(96) = 97 instead of 95). - _Franklin T. Adams-Watters_, Sep 01 2006
%H Reinhard Zumkeller, <a href="/A091857/b091857.txt">Table of n, a(n) for n = 1..10000</a>
%o (Haskell)
%o import Data.List (delete)
%o a091857 n = a091857_list !! (n-1)
%o a091857_list = 1 : f 1 1 [2..] where
%o f 1 z xs = g xs where
%o g (u:us) = if gcd u z == 1 then u : f 0 u (delete u xs) else g us
%o f 0 z xs = h xs where
%o h (v:vs) = if gcd v z /= 1 then v : f 1 v (delete v xs) else h vs
%o -- _Reinhard Zumkeller_, Feb 17 2015
%Y Cf. A091856.
%K easy,nonn
%O 1,2
%A _Amarnath Murthy_, Mar 13 2004
%E More terms from _Franklin T. Adams-Watters_, Sep 01 2006
%E Data corrected for n > 52 by _Reinhard Zumkeller_, Feb 17 2015
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