A005244 A self-generating sequence: start with 2 and 3, take all products of any 2 previous elements, subtract 1 and adjoin them to the sequence. (Formerly M0704)

2, 3, 5, 9, 14, 17, 26, 27, 33, 41, 44, 50, 51, 53, 65, 69, 77, 80, 81, 84, 87, 98, 99, 101, 105, 122, 125, 129, 131, 134, 137, 149, 152, 153, 158, 159, 161, 164, 167, 173, 194, 195, 197, 201, 204, 206, 209, 219, 230, 233, 237, 239, 242, 243, 249

Offset

1,1

Comments

a(n) = A139127(n)*a(k)-1 for some k; A139128 gives number of distinct representations a(n) = a(i)*a(j)-1. - Reinhard Zumkeller, Apr 09 2008

Complement of A171413. [Jaroslav Krizek, Dec 08 2009]

References

R. K. Guy, Unsolved Problems in Number Theory, E31.

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

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Thomas Bloom, Problem 424, Erdős Problems.

Eric Weisstein's World of Mathematics, Hofstadter Sequences.

Example

17 is present because it equals 2*9-1.

Mathematica

f[s_, mx_] := Union[s, Select[Apply[Times, Subsets[s, {2}], {1}] - 1, # <= mx &]]; mx = 250; FixedPoint[f[#, mx] &, {2, 3}] (* Jean-François Alcover, Mar 29 2011 *)

Prog

(Haskell)
import Data.Set (singleton, deleteFindMin, fromList, union)
a005244 n = a005244_list !! (n-1)
a005244_list = f [2] (singleton 2) where
   f xs s = y :
     f (y : xs) (s' `union` fromList (map ((subtract 1) . (* y)) xs))
     where (y, s') = deleteFindMin s
-- Reinhard Zumkeller, Feb 26 2013

Crossrefs

Cf. A139127, A139128, A171413.

Sequence in context: A220315 A070819 A195667 * A058541 A023672 A023567

Adjacent sequences: A005241 A005242 A005243 * A005245 A005246 A005247

Keyword

nonn,nice,easy

Author

D. R. Hofstadter

Extensions

More terms from Jud McCranie

Status

approved