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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.

%I A285763 #9 Apr 26 2017 22:43:21
%S A285763 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,
%T A285763 16,16,16,16,17,18,19,20,21,22,23,24,24,24,25,26,27,28,28,28,29,30,30,
%U A285763 30,30,30,31,32,32,32,32,32,32,32,32,32
%N 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.
%C A285763 The sequence a(n) is monotonic, with successive terms increasing by 0 or 1. So the sequence hits every positive integer.
%C A285763 This sequence can be obtained from the Hofstadter-Conway sequence A004001 using a construction of Isgur et al.
%H A285763 Nathan Fox, <a href="/A285763/b285763.txt">Table of n, a(n) for n = 1..10000</a>
%H A285763 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 A285763 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:
%t A285763 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 *)
%Y A285763 Cf. A004001, A285764.
%K A285763 nonn
%O A285763 1,2
%A A285763 _Nathan Fox_, Apr 25 2017