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A285764
A relative of the Hofstadter-Conway sequence A004001.
2
1, 2, 3, 3, 3, 3, 4, 5, 6, 6, 6, 6, 7, 8, 9, 10, 11, 12, 12, 12, 12, 12, 12, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 21, 21, 21, 22, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 36, 36, 36, 37
OFFSET
1,2
COMMENTS
a(n) is the solution to the recurrence relation a(n) = a(a(n-3)) + a(n-a(n-3)), with the initial conditions: a(1) = 1, a(2) = 2, a(3) = a(4) = a(5) = a(6) = 3, a(7) = 4, a(8) = 5, a(9) = 6.
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 the Hofstadter-Conway sequence A004001 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
A285764:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 1: elif n = 2 then 2: elif n = 3 then 3: elif n = 4 then 3: elif n = 5 then 3: elif n = 6 then 3: elif n = 7 then 4: elif n = 8 then 5: elif n = 9 then 6: else A285764(A285764(n-3)) + A285764(n-A285764(n-3)): fi: end:
CROSSREFS
Sequence in context: A255070 A176001 A194272 * A025776 A120505 A029109
KEYWORD
nonn
AUTHOR
Nathan Fox, Apr 25 2017
STATUS
approved