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A274429 Numbers that are a product of two distinct Fibonacci numbers >1 or two distinct Lucas numbers > 0 (excluding 2).

%I A274429 #5 Jun 22 2016 23:16:03
%S A274429 3,4,6,7,10,11,12,15,16,18,21,24,26,28,29,33,39,40,42,44,47,54,63,65,
%T A274429 68,72,76,77,87,102,104,105,110,116,123,126,141,165,168,170,178,188,
%U A274429 198,199,203,228,267,272,273,275,288,304,319,322,329,369,432,440
%N A274429 Numbers that are a product of two distinct Fibonacci numbers >1 or two distinct Lucas numbers > 0 (excluding 2).
%C A274429 Let U = {F(i)F(j), 2 < i < j}, where F = A000045 (Fibonacci numbers), and V = {L(i)L(j), 0 < i < j}, where L = A000032 (Lucas numbers).  The sets U and V are disjoint, and their union, arranged as a sequence in increasing order, is A274429.  (Unlike A274426, here all the Lucas numbers except 1 are included.)
%C A274429 Writing u for a Fibonacci product and v for a Lucas product, the numbers in A274429 are represented by the infinite word vvuvuvvuuvvuuvvvuuuvvvuuuvvvv...  This is the concatenation of v and the words (v^k)(u^k)(v^k)(u^k) for k >= 1.  Thus, there are runs of Fibonacci products of every finite length and runs of Lucas products of every finite length.
%C A274429 See A274426 for a guide to related sequences.
%t A274429 z = 200; f[n_] := Fibonacci[n];
%t A274429 u = Take[Sort[Flatten[Table[f[m] f[n], {n, 3, z}, {m, 3, n - 1}]]], 100]
%t A274429 g[n_] := LucasL[n];
%t A274429 v = Take[Sort[Flatten[Table[g[u] g[v], {u, 1, z}, {v, 1, u - 1}]]], z]
%t A274429 Intersection[u, v]
%t A274429 w = Union[u, v]  (* A274429 *)
%t A274429 Select[Range[300], MemberQ[u, w[[#]]] &]  (* A274430 *)
%t A274429 Select[Range[300], MemberQ[v, w[[#]]] &]  (* A274431 *)
%Y A274429 Cf. A274430 (positions of numbers in U), A274431 (positions of numbers in V), A000032, A000045, A274426.
%K A274429 nonn,easy
%O A274429 1,1
%A A274429 _Clark Kimberling_, Jun 22 2016