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Unique increasing sequence satisfying a(n) = a(n-3) + c(n-3); where c( ) is complement of a( ).
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%I #9 Apr 05 2016 10:25:58

%S 1,2,3,5,8,10,14,19,22,27,34,38,44,52,58,65,75,82,90,101,110,119,131,

%T 141,151,164,176,187,201,215,227,242,257,270,287,303,317,335,352,367,

%U 386,405,421,441,461,478,500,521,539,562,584,603,628,651

%N Unique increasing sequence satisfying a(n) = a(n-3) + c(n-3); where c( ) is complement of a( ).

%C Here "complement" refers to the numbers not in the sequence.

%H Ivan Neretin, <a href="/A022955/b022955.txt">Table of n, a(n) for n = 1..10000</a>

%t Fold[Append[#1, #1[[#2]] + Complement[Range[Max@#1 + 1], #1][[#2]]] &, {1, 2, 3}, Range[50]] (* _Ivan Neretin_, Apr 05 2016 *)

%Y Cf. A005228 and references therein.

%K nonn

%O 1,2

%A _Clark Kimberling_