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A274429 Numbers that are a product of two distinct Fibonacci numbers >1 or two distinct Lucas numbers > 0 (excluding 2). 4
3, 4, 6, 7, 10, 11, 12, 15, 16, 18, 21, 24, 26, 28, 29, 33, 39, 40, 42, 44, 47, 54, 63, 65, 68, 72, 76, 77, 87, 102, 104, 105, 110, 116, 123, 126, 141, 165, 168, 170, 178, 188, 198, 199, 203, 228, 267, 272, 273, 275, 288, 304, 319, 322, 329, 369, 432, 440 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.)

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.

See A274426 for a guide to related sequences.

LINKS

Table of n, a(n) for n=1..58.

MATHEMATICA

z = 200; f[n_] := Fibonacci[n];

u = Take[Sort[Flatten[Table[f[m] f[n], {n, 3, z}, {m, 3, n - 1}]]], 100]

g[n_] := LucasL[n];

v = Take[Sort[Flatten[Table[g[u] g[v], {u, 1, z}, {v, 1, u - 1}]]], z]

Intersection[u, v]

w = Union[u, v]  (* A274429 *)

Select[Range[300], MemberQ[u, w[[#]]] &]  (* A274430 *)

Select[Range[300], MemberQ[v, w[[#]]] &]  (* A274431 *)

CROSSREFS

Cf. A274430 (positions of numbers in U), A274431 (positions of numbers in V), A000032, A000045, A274426.

Sequence in context: A102093 A135215 A092494 * A050618 A093579 A060832

Adjacent sequences:  A274426 A274427 A274428 * A274430 A274431 A274432

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 22 2016

STATUS

approved

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Last modified July 4 16:24 EDT 2020. Contains 335448 sequences. (Running on oeis4.)