cp's OEIS Frontend

A285761 A slow relative of Hofstadter's Q sequence.

%I A285761 #6 Apr 26 2017 22:43:30
%S A285761 1,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,8,8,8,9,9,10,10,10,11,11,12,12,12,13,
%T A285761 13,14,15,15,15,16,16,16,17,17,18,19,19,19,20,20,20,21,21,22,23,23,23,
%U A285761 24,24,24,25,25,26,27,27,28,28,29,29
%N A285761 A slow relative of Hofstadter's Q sequence.
%C A285761 a(n) is the solution to the recurrence relation a(n) = a(n-4-a(n-1)) + a(n-4-a(n-4)), with the initial conditions: a(1) = 1, a(2) = 2, a(3) = a(4) = a(5) = 3, a(6) = a(7) = a(8) = 4, a(9) = a(10) = 5.
%C A285761 The sequence a(n) is monotonic, with successive terms increasing by 0 or 1. So the sequence hits every positive integer.
%H A285761 Nathan Fox, <a href="/A285761/b285761.txt">Table of n, a(n) for n = 1..10000</a>
%H A285761 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 A285761 A285761:=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 4: elif n = 7 then 4: elif n = 8 then 4: elif n = 9 then 5: elif n = 10 then 5: else A285761(n-4-A285761(n-1)) + A285761(n-4-A285761(n-4)): fi: end:
%Y A285761 Cf. A005185, A063882, A285757, A285758, A285759, A285760, A285762.
%K A285761 nonn
%O A285761 1,2
%A A285761 _Nathan Fox_, Apr 25 2017