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A009388 If a, b in sequence, so is a*b-1.

%I A009388 #23 Sep 01 2016 13:15:37
%S A009388 2,3,5,8,9,14,15,17,23,24,26,27,29,33,39,41,44,45,47,50,51,53,57,63,
%T A009388 65,68,69,71,74,77,80,81,84,86,87,89,93,98,99,101,105,111,113,114,116,
%U A009388 119,122,125,129,131,134,135,137,140,141,144,147,149,152,153,158,159,161,164
%N A009388 If a, b in sequence, so is a*b-1.
%C A009388 All terms are congruent to 0 or 2 mod 3. It follows that no three consecutive integers are in the sequence. - _Franklin T. Adams-Watters_, Aug 31 2016, conjectured by _David W. Wilson_.
%H A009388 Reinhard Zumkeller, <a href="/A009388/b009388.txt">Table of n, a(n) for n = 1..1000</a>
%t A009388 f[l_] := Block[{k = l}, Select[ Union[ Flatten[ AppendTo[k, Table[ k[[i]]*k[[j]] - 1, {i, 1, Length[k]}, {j, 1, i}]]]], # < 170 &]]; NestList[f, {2}, 6][[ -1]] (* _Robert G. Wilson v_, May 23 2004 *)
%o A009388 (Haskell)
%o A009388 import Data.Set (singleton, deleteFindMin, insert)
%o A009388 a009388 n = a009388_list !! (n-1)
%o A009388 a009388_list = f [2] (singleton 2) where
%o A009388    f xs s = m : f xs' (foldl (flip insert) s' (map (pred . (* m)) xs'))
%o A009388      where xs' = m : xs
%o A009388            (m,s') = deleteFindMin s
%o A009388 -- _Reinhard Zumkeller_, Aug 15 2011
%Y A009388 Cf. A009293. This is superset of A005659 - 1.
%Y A009388 Cf. A009299, A192476.
%K A009388 nonn
%O A009388 1,1
%A A009388 _David W. Wilson_