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a(n) = a(n-2) + c(n-1) for n >= 3, a( ) increasing, given a(1)=2, a(2)=4; where c( ) is complement of a( ).
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%I #7 Apr 06 2016 12:02:30

%S 2,4,5,10,12,18,21,29,34,43,49,59,66,78,86,100,109,124,134,150,161,

%T 178,191,209,223,242,258,278,295,316,334,356,375,398,419,443,465,490,

%U 513,540,564,592,617,646,672,702,729,760,789,821,851,884,915

%N a(n) = a(n-2) + c(n-1) for n >= 3, a( ) increasing, given a(1)=2, a(2)=4; where c( ) is complement of a( ).

%H Ivan Neretin, <a href="/A022944/b022944.txt">Table of n, a(n) for n = 1..10000</a>

%t Fold[Append[#1, #1[[-2]] + Complement[Range[Max@#1 + 2], #1][[#2]]] &, {2, 4}, Range[2, 52]] (* _Ivan Neretin_, Apr 05 2016 *)

%Y Cf. A005228 and references therein.

%K nonn

%O 1,1

%A _Clark Kimberling_