A003669 a(n) is smallest number which is uniquely a(j) + a(k), j < k. (Formerly M2339)

3, 4, 7, 10, 11, 13, 15, 16, 21, 22, 27, 30, 35, 36, 41, 44, 50, 53, 55, 61, 69, 70, 75, 78, 84, 87, 92, 93, 98, 101, 107, 112, 118, 121, 132, 135, 138, 141, 149, 150, 164, 166, 169, 175, 178, 189, 192, 195, 197, 198, 206, 212, 215, 223, 232, 252, 254, 255, 263, 269

Offset

1,1

Comments

An Ulam-type sequence - see A002858 for many further references, comments, etc. - T. D. Noe, Jan 21 2008

References

R. K. Guy, "s-Additive sequences", preprint, 1994.

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

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

S. R. Finch, Patterns in 1-additive sequences, Experimental Mathematics 1 (1992), 57-63.

R. K. Guy, s-Additive sequences, Preprint, 1994. (Annotated scanned copy)

Eric Weisstein's World of Mathematics, Ulam Sequence

Wikipedia, Ulam number

Index entries for Ulam numbers

Mathematica

Nest[Append[#, SelectFirst[Union@ Select[Tally@ Map[Total, Select[Permutations[#, {2}], #1 < #2 & @@ # &]], Last@ # == 1 &][[All, 1]], Function[k, FreeQ[#, k]]]] &, {3, 4}, 58] (* Michael De Vlieger, Nov 16 2017 *)

Prog

(Haskell)
a003669 n = a003669_list !! (n-1)
a003669_list = 3 : 4 : ulam 2 4 a003669_list
-- Function ulam as defined in A002858.
-- Reinhard Zumkeller, Nov 03 2011

Crossrefs

Sequence in context: A359394 A295399 A257507 * A047342 A334469 A228854

Adjacent sequences: A003666 A003667 A003668 * A003670 A003671 A003672

Keyword

nonn

Author

N. J. A. Sloane, Mira Bernstein

Status

approved