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

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

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn

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

Programs

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

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 *)