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a(n) = a(n-1) + c(n-1) for n >= 2, a( ) increasing, given a(1)=3, where c( ) is complement of a( ).
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%I #22 Sep 16 2015 02:01:47

%S 3,4,6,11,18,26,35,45,57,70,84,99,115,132,151,171,192,214,237,261,286,

%T 313,341,370,400,431,463,496,530,566,603,641,680,720,761,803,846,890,

%U 936,983,1031,1080,1130,1181,1233,1286,1340,1395,1451,1509

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

%C Complement means that c(i) is the i-th member of the sorted list of integers >=1 that are not in the set {a(1),...,a(i-1)}. - _R. J. Mathar_, Aug 06 2015

%H Vincenzo Librandi, <a href="/A022935/b022935.txt">Table of n, a(n) for n = 1..1000</a>

%t mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;

%t a[1] = 3; c[1] = 1; c[2] = 2;

%t a[n_] := a[n] = a[n - 1] + c[n - 1];

%t c[n_] := c[n] = mex[Flatten[Table[{a[i], c[i]}, {i, 1, n - 1}]]];

%t Table[a[n], {n, 80}] (* A022935 *)

%t Table[c[n], {n, 80}]

%t (* _Clark Kimberling_, May 15 2012 *)

%K nonn

%O 1,1

%A _Clark Kimberling_