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A329311
a(n) is the product of the numbers k such that a(n-2*k) = a(n-k) and 0 < n-2*k < n-k < n.
2
1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 8, 10, 90, 42, 42, 56, 56, 72, 9, 10, 1, 1, 1, 1, 2, 2, 3, 8, 1, 1, 1, 11, 24, 780, 1092, 7644, 11760, 11760, 311040, 2736, 64600, 420, 420, 462, 157080, 10626, 483, 210672, 20, 420, 462, 462, 506, 23, 624, 27, 5292, 45472, 812
OFFSET
1,5
COMMENTS
This sequence has fractal features; apparently, for any k > 0, the first k terms are repeated later (see illustration in Links section).
LINKS
Rémy Sigrist, Logarithmic scatterplot of the first 80000 terms (the two colored sections are equal up to an horizontal shift)
EXAMPLE
The first terms, alongside the corresponding k's, are:
n a(n) k's
--- ------- ---------
1 1 {}
2 1 {}
3 1 {1}
4 1 {1}
5 2 {1, 2}
6 2 {2}
7 3 {1, 3}
8 1 {}
9 1 {}
10 1 {1}
11 1 {1}
12 8 {1, 2, 4}
13 10 {2, 5}
14 90 {3, 5, 6}
15 42 {6, 7}
16 42 {6, 7}
17 56 {1, 7, 8}
PROG
(PARI) for (n=1, #(a=vector(60)), print1 (a[n] = prod(k=1, (n-1)\2, if (a[n-k]==a[n-2*k], k, 1)) ", "))
CROSSREFS
See A329257 for similar sequences.
Sequence in context: A084189 A084352 A106797 * A308746 A367125 A074313
KEYWORD
nonn,look
AUTHOR
Rémy Sigrist, Nov 10 2019
STATUS
approved