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a(n) = c(n-1) + c(n-3) where c is the sequence of numbers not in a.
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%I #6 Mar 29 2017 20:28:55

%S 1,2,5,9,11,14,17,20,23,27,29,33,35,39,41,45,47,50,53,56,59,62,65,68,

%T 71,74,77,80,83,86,89,92,95,99,101,105,107,111,113,117,119,123,125,

%U 129,131,135,137

%N a(n) = c(n-1) + c(n-3) where c is the sequence of numbers not in a.

%H Ivan Neretin, <a href="/A022429/b022429.txt">Table of n, a(n) for n = 0..10000</a>

%t Fold[Append[#1, Plus @@ Complement[Range[Max@#1 + 3], #1][[{#2, #2 + 2}]]] &, {1, 2, 5}, Range[43]] (* _Ivan Neretin_, Mar 29 2017 *)

%Y Cf. A022424 and references therein.

%K nonn

%O 0,2

%A _Clark Kimberling_

%E Missing term a(20) = 59 added by _Ivan Neretin_, Mar 29 2017