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

2, 3, 5, 8, 9, 14, 15, 17, 23, 24, 26, 27, 29, 33, 39, 41, 44, 45, 47, 50, 51, 53, 57, 63, 65, 68, 69, 71, 74, 77, 80, 81, 84, 86, 87, 89, 93, 98, 99, 101, 105, 111, 113, 114, 116, 119, 122, 125, 129, 131, 134, 135, 137, 140, 141, 144, 147, 149, 152, 153, 158, 159, 161, 164

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

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.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

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

Cf. A009299, A192476.

Programs

Haskell

import Data.Set (singleton, deleteFindMin, insert)
a009388 n = a009388_list !! (n-1)
a009388_list = f [2] (singleton 2) where
   f xs s = m : f xs' (foldl (flip insert) s' (map (pred . (* m)) xs'))
     where xs' = m : xs
           (m,s') = deleteFindMin s
-- Reinhard Zumkeller, Aug 15 2011

Mathematica

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 *)