

A272907


Lucasproducts fractal sequence.


3



1, 1, 1, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 4, 2, 3, 1, 4, 2, 3, 5, 1, 4, 2, 3, 5, 1, 4, 2, 3, 5, 1, 6, 4, 2, 3, 5, 1, 6, 4, 2, 3, 5, 7, 1, 6, 4, 2, 3, 5, 7, 1, 6, 4, 2, 3, 5, 7, 1, 8, 6, 4, 2, 3, 5, 7, 1, 8, 6, 4, 2, 3, 5, 7, 9, 1, 8, 6, 4, 2, 3, 5, 7, 9
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OFFSET

1,5


COMMENTS

Let L = A000032, the Lucas numbers. Let s be the sequence of all products L(i)L(j), for 1 <= i < = j, arranged in increasing order; viz., (1,3,4,7,9,11,12,16,18,21,...) = (L(1)L(1), L(1)L(2), L(1)L(3), L(1)L(4), L(2)L(2), L(1)L(5), L(2)L(3), L(3)L(3), L(1)L(6), L(2)L(4),...). The sequence of first factors is represented by indices A272907 = (1,1,1,1,2,1,2,3,1,2,...), which is a fractal sequence; i.e., the removal of the first occurrence of each term in A272907 leaves A272907, so that the sequence contains itself infinitely many times.


LINKS



MATHEMATICA

z = 200; f[n_] := LucasL[n]; u1 = Table[f[n], {n, 1, z}];
u2 = Sort[Flatten[Table[f[i]*f[j], {i, 1, z}, {j, i, z}]]];
Table[Select[Range[30], MemberQ[u1, u2[[i]]/f[#]] &][[1]], {i, 1, z}]


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



