%I #7 Feb 22 2020 20:54:24
%S 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,
%T 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,
%U 1,8,6,4,2,3,5,7,9,1,8,6,4,2,3,5,7,9
%N Lucasproducts fractal sequence.
%C 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.
%H Clark Kimberling, <a href="/A272907/b272907.txt">Table of n, a(n) for n = 1..1000</a>
%t z = 200; f[n_] := LucasL[n]; u1 = Table[f[n], {n, 1, z}];
%t u2 = Sort[Flatten[Table[f[i]*f[j], {i, 1, z}, {j, i, z}]]];
%t Table[Select[Range[30], MemberQ[u1, u2[[i]]/f[#]] &][[1]], {i, 1, z}]
%Y Cf. A272908 (associated interspersion), A000032, A272900 (Fibonacciproducts fractal sequence).
%K nonn,easy
%O 1,5
%A _Clark Kimberling_, May 10 2016
