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a(n) = b(n) - c(n) where b(n) is the n-th Lucas number greater than 3 and c(n) is the n-th number not in sequence b( ).
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%I #12 Jun 20 2019 19:36:47

%S 3,5,8,13,23,39,67,113,187,309,507,828,1348,2190,3552,5758,9328,15105,

%T 24453,39579,64054,103656,167734,271415,439174,710616,1149819,1860465,

%U 3010315,4870812,7881160,12752006,20633201,33385243,54018481

%N a(n) = b(n) - c(n) where b(n) is the n-th Lucas number greater than 3 and c(n) is the n-th number not in sequence b( ).

%H G. C. Greubel, <a href="/A014252/b014252.txt">Table of n, a(n) for n = 1..1000</a>

%t b:= Complement[Range[1, 100], LucasL[Range[20]]]; Join[{3, 5, 8}, Table[LucasL[n+4] - b[[n]], {n,2,35}]] (* _G. C. Greubel_, Jun 19 2019 *)

%Y Cf. A000032 (Lucas numbers).

%K nonn

%O 1,1

%A _Clark Kimberling_

%E Missing a(30) inserted and more terms from _Sean A. Irvine_, Oct 17 2018