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If a, b in sequence, so is a*b-1.
4

%I #23 Sep 01 2016 13:15:37

%S 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 65,68,69,71,74,77,80,81,84,86,87,89,93,98,99,101,105,111,113,114,116,

%U 119,122,125,129,131,134,135,137,140,141,144,147,149,152,153,158,159,161,164

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

%C 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 Reinhard Zumkeller, <a href="/A009388/b009388.txt">Table of n, a(n) for n = 1..1000</a>

%t 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 (Haskell)

%o import Data.Set (singleton, deleteFindMin, insert)

%o a009388 n = a009388_list !! (n-1)

%o a009388_list = f [2] (singleton 2) where

%o f xs s = m : f xs' (foldl (flip insert) s' (map (pred . (* m)) xs'))

%o where xs' = m : xs

%o (m,s') = deleteFindMin s

%o -- _Reinhard Zumkeller_, Aug 15 2011

%Y Cf. A009293. This is superset of A005659 - 1.

%Y Cf. A009299, A192476.

%K nonn

%O 1,1

%A _David W. Wilson_