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 A272907 Lucas-products 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 7 17:47 EDT 2024. Contains 375017 sequences. (Running on oeis4.)