%I #7 Apr 26 2017 02:49:48

%S 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,

%T 17,18,19,20,21,21,21,21,22,23,24,24,24,24,24,24,24,24,24,24,25,26,27,

%U 28,29,30,31,32,33,34,35,36,36,36,36,37

%N A relative of the Hofstadter-Conway sequence A004001.

%C 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.

%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 the Hofstadter-Conway sequence A004001 using a construction of Isgur et al.

%H Nathan Fox, <a href="/A285764/b285764.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 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:

%Y Cf. A004001, A285763.

%K nonn

%O 1,2

%A _Nathan Fox_, Apr 25 2017