cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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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.

Crossrefs

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

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 *)

A005661 k in S implies 2k-2, 3k-3 in S.

Original entry on oeis.org

5, 8, 12, 14, 21, 22, 26, 33, 39, 40, 42, 50, 60, 63, 64, 75, 76, 78, 82, 96, 98, 114, 117, 118, 123, 124, 126, 147, 148, 150, 154, 162, 177, 186, 189, 190, 194, 222, 225, 226, 231, 232, 234, 243, 244, 246, 250, 285, 291, 292, 294, 298, 306, 322, 339, 348, 351
Offset: 1

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Author

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Examples

			From _Seiichi Manyama_, Feb 29 2024: (Start)
663, 994 and 1986 are terms and 1986 = 2*994 - 2 = 3*663 - 3.
3159, 4738 and 9474 are terms and 9474 = 2*4738 - 2 = 3*3159 - 3.
18711, 28066 and 56130 are terms and 56130 = 2*28066 - 2 = 3*18711 - 3. (End)
		

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Cf. A005659.

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Oct 01 2001
Showing 1-2 of 2 results.