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a(n) = a(n - a(n - 2)) + a(n - a(n - 8)), with a(i) = i for 1 <= i <= 9.
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%I #8 Apr 26 2017 22:34:45

%S 1,2,3,4,5,6,7,8,9,10,10,10,11,12,12,12,13,14,15,16,16,16,17,18,18,18,

%T 19,20,21,22,22,22,22,22,23,24,24,24,25,26,27,28,28,28,29,30,30,30,31,

%U 32,33,34,34,34,34,34,35,36,36,36,37,38,39

%N a(n) = a(n - a(n - 2)) + a(n - a(n - 8)), with a(i) = i for 1 <= i <= 9.

%C The sequence a(n) is monotonic, with successive terms increasing by 0 or 1. So the sequence hits every positive integer.

%C This sequence can be obtained from A063882 using a construction of Isgur et al.

%H Nathan Fox, <a href="/A285757/b285757.txt">Table of n, a(n) for n = 1..10000</a>

%H A. Isgur, R. Lech, S. Moore, S. Tanny, Y. Verberne, and Y. Zhang, <a href="http://dx.doi.org/10.1137/15M1040505">Constructing New Families of Nested Recursions with Slow Solutions</a>, SIAM J. Discrete Math., 30(2), 2016, 1128-1147. (20 pages); DOI:10.1137/15M1040505

%p A285757:=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 4: elif n = 5 then 5: elif n = 6 then 6: elif n = 7 then 7: elif n = 8 then 8: elif n = 9 then 9: else A285757(n-A285757(n-2)) + A285757(n-A285757(n-8)): fi: end:

%Y Cf. A005185, A063882, A285758, A285759, A285760, A285761, A285762.

%K nonn

%O 1,2

%A _Nathan Fox_, Apr 25 2017