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%I #17 Jul 25 2024 14:48:46
%S 1,2,4,7,13,19,29,37,43,49,58,61,67,73,79,89,97,103,109,127,133,139,
%T 149,157,163,169,179,193,199,211,223,229,239,247,259,271,277,283,293,
%U 298,301,307,313,331,337,343,349,358,361,367,373,379,397,409,421,427,433
%N a(1)=1, a(2)=2; for n > 2, a(n) is the smallest m that has not yet appeared and is not divisible by any pairwise sum of a(1)..a(n-1).
%C Strictly increasing sequence.
%e a(1)=1, a(2)=2, a(3)=4, pairwise sums=pws={3,5,6}; smallest m that has not yet appeared and is not divisible by any of pws is m=7 hence a(4)=7; now pws={3,5,6,8,9,11}; hence a(5)=13, etc.
%t s={1,2}; ps={3}; a=2; Do[Do[If[Mod[n,ps[[i]]]==0,Goto[ne]], {i,Length[ps]}]; a=n; ps=Union[Flatten[{ps,s+a}]]; AppendTo[s,a]; Label[ne],{n,3,1000}]; s
%o (PARI) {S=[]; for(n=1,999, for(i=2,#S, for(j=1,i-1, n%(S[i]+S[j]) || next(3))); S=concat(S,n); print1(n","))} \\ _M. F. Hasler_, Aug 30 2009
%Y Cf. A164901.
%K nonn
%O 1,2
%A _Zak Seidov_, Jul 14 2009
%E Terms corrected by _M. F. Hasler_, Aug 30 2009