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A285763
a(n) = a(a(n - 2)) + a(n - a(n - 2)), with a(1) = 1, a(2) = a(3) = a(4) = 2, a(5) = 3.
2
1, 2, 2, 2, 3, 4, 4, 4, 5, 6, 7, 8, 8, 8, 8, 8, 9, 10, 11, 12, 13, 14, 14, 14, 15, 16, 16, 16, 16, 16, 16, 16, 17, 18, 19, 20, 21, 22, 23, 24, 24, 24, 25, 26, 27, 28, 28, 28, 29, 30, 30, 30, 30, 30, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32
OFFSET
1,2
COMMENTS
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
A285763:=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 3: else A285763(A285763(n-2)) + A285763(n-A285763(n-2)): fi: end:
MATHEMATICA
a[1] = 1; a[2] = a[3] = a[4] = 2; a[5] = 3; a[n_] := a[n] = a[a[n - 2]] + a[n - a[n - 2]]; Array[a, 64] (* Michael De Vlieger, Apr 26 2017 *)
CROSSREFS
Sequence in context: A126257 A025773 A308303 * A294621 A029077 A112176
KEYWORD
nonn
AUTHOR
Nathan Fox, Apr 25 2017
STATUS
approved