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A285758
A slow relative of Hofstadter's Q sequence.
6
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
OFFSET
1,2
COMMENTS
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.
LINKS
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
MAPLE
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:
KEYWORD
nonn
AUTHOR
Nathan Fox, Apr 25 2017
STATUS
approved