A272907 Lucas-products fractal sequence.

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

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

Clark Kimberling, Table of n, a(n) for n = 1..1000

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

Cf. A272908 (associated interspersion), A000032, A272900 (Fibonacci-products fractal sequence).

Sequence in context: A357554 A199086 A098053 * A128117 A373212 A023115

Adjacent sequences: A272904 A272905 A272906 * A272908 A272909 A272910

Keyword

nonn,easy

Author

Clark Kimberling, May 10 2016

Status

approved