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A285758
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A slow relative of Hofstadter's Q sequence.
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6
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1, 2, 2, 2, 2, 2, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 11, 12, 12, 12, 13, 14, 15, 16, 16, 16, 17, 18, 18, 18, 19, 20, 21, 22, 22, 22, 22, 22, 23, 24, 24, 24, 25, 26, 27, 28, 28, 28, 29, 30, 30, 30, 31, 32, 33, 34, 34, 34, 34, 34, 35, 36
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OFFSET
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1,2
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COMMENTS
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a(n) is the solution to the recurrence relation a(n) = a(n-a(n-2)) + a(n-a(n-8)), with the initial conditions: a(1) = 1, a(i) = 2 for 2 <= i <= 8, and a(9) = 3.
The sequence a(n) is monotonic, with successive terms increasing by 0 or 1. So the sequence hits every positive integer.
This sequence can be obtained from A063882 using a construction of Isgur et al.
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LINKS
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A. Isgur, R. Lech, S. Moore, S. Tanny, Y. Verberne, and Y. Zhang, Constructing New Families of Nested Recursions with Slow Solutions, SIAM J. Discrete Math., 30(2), 2016, 1128-1147. (20 pages); DOI:10.1137/15M1040505
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MAPLE
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A285758:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 1: elif n = 2 then 2: elif n = 3 then 2: elif n = 4 then 2: elif n = 5 then 2: elif n = 6 then 2: elif n = 7 then 2: elif n = 8 then 2: elif n = 9 then 3: else A285758(n-A285758(n-2)) + A285758(n-A285758(n-8)): fi: end:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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