cp's OEIS Frontend

A285758 A slow relative of Hofstadter's Q sequence.

%I A285758 #7 Apr 26 2017 22:42:48
%S A285758 1,2,2,2,2,2,2,2,3,4,5,6,7,8,9,10,10,10,11,12,12,12,13,14,15,16,16,16,
%T A285758 17,18,18,18,19,20,21,22,22,22,22,22,23,24,24,24,25,26,27,28,28,28,29,
%U A285758 30,30,30,31,32,33,34,34,34,34,34,35,36
%N A285758 A slow relative of Hofstadter's Q sequence.
%C A285758 a(n) is the solution to the recurrence relation a(n) = a(n-a(n-2)) + a(n-a(n-8)), with the initial conditions: a(1) = 1, a(i) = 2 for 2 <= i <= 8, and a(9) = 3.
%C A285758 The sequence a(n) is monotonic, with successive terms increasing by 0 or 1. So the sequence hits every positive integer.
%C A285758 This sequence can be obtained from A063882 using a construction of Isgur et al.
%H A285758 Nathan Fox, <a href="/A285758/b285758.txt">Table of n, a(n) for n = 1..10000</a>
%H A285758 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 A285758 A285758:=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 2: elif n = 6 then 2: elif n = 7 then 2: elif n = 8 then 2: elif n = 9 then 3: else A285758(n-A285758(n-2)) + A285758(n-A285758(n-8)): fi: end:
%Y A285758 Cf. A005185, A063882, A285757, A285759, A285760, A285761, A285762.
%K A285758 nonn
%O A285758 1,2
%A A285758 _Nathan Fox_, Apr 25 2017