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

%I A003669 M2339 #35 Feb 16 2025 08:32:27
%S A003669 3,4,7,10,11,13,15,16,21,22,27,30,35,36,41,44,50,53,55,61,69,70,75,78,
%T A003669 84,87,92,93,98,101,107,112,118,121,132,135,138,141,149,150,164,166,
%U A003669 169,175,178,189,192,195,197,198,206,212,215,223,232,252,254,255,263,269
%N A003669 a(n) is smallest number which is uniquely a(j) + a(k), j < k.
%C A003669 An Ulam-type sequence - see A002858 for many further references, comments, etc. - _T. D. Noe_, Jan 21 2008
%D A003669 R. K. Guy, "s-Additive sequences", preprint, 1994.
%D A003669 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003669 T. D. Noe, <a href="/A003669/b003669.txt">Table of n, a(n) for n = 1..10000</a>
%H A003669 S. R. Finch, <a href="http://www.emis.de/journals/EM/expmath/volumes/1/1.html">Patterns in 1-additive sequences</a>, Experimental Mathematics 1 (1992), 57-63.
%H A003669 R. K. Guy, <a href="/A007300/a007300.pdf">s-Additive sequences</a>, Preprint, 1994. (Annotated scanned copy)
%H A003669 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UlamSequence.html">Ulam Sequence</a>
%H A003669 Wikipedia, <a href="http://en.wikipedia.org/wiki/Ulam_number">Ulam number</a>
%H A003669 <a href="/index/U#Ulam_num">Index entries for Ulam numbers</a>
%t A003669 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 *)
%o A003669 (Haskell)
%o A003669 a003669 n = a003669_list !! (n-1)
%o A003669 a003669_list = 3 : 4 : ulam 2 4 a003669_list
%o A003669 -- Function ulam as defined in A002858.
%o A003669 -- _Reinhard Zumkeller_, Nov 03 2011
%K A003669 nonn
%O A003669 1,1
%A A003669 _N. J. A. Sloane_, _Mira Bernstein_