|
%I #7 Apr 26 2017 22:43:13
%S 1,2,3,4,5,6,7,8,9,9,9,9,9,9,9,10,11,12,12,12,12,12,12,12,13,14,15,15,
%T 15,15,15,15,15,16,17,18,18,18,18,18,18,18,19,20,21,21,21,21,22,23,24,
%U 24,24,24,24,24,24,25,26,27,27,27,27,28
%N A slow relative of Hofstadter's Q sequence.
%C a(n) is the solution to the recurrence relation a(n) = a(n-12-a(n-3)) + a(n-12-a(n-12)), with a(1) through a(33) as initial conditions.
%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 A285761 using a construction of Isgur et al.
%H Nathan Fox, <a href="/A285762/b285762.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 A285762:=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: elif n = 10 then 9: elif n = 11 then 9: elif n = 12 then 9: elif n = 13 then 9: elif n = 14 then 9: elif n = 15 then 9: elif n = 16 then 10: elif n = 17 then 11: elif n = 18 then 12: elif n = 19 then 12: elif n = 20 then 12: elif n = 21 then 12: elif n = 22 then 12: elif n = 23 then 12: elif n = 24 then 12: elif n = 25 then 13: elif n = 26 then 14: elif n = 27 then 15: elif n = 28 then 15: elif n = 29 then 15: elif n = 30 then 15: elif n = 31 then 15: elif n = 32 then 15: elif n = 33 then 15: else A285762(n-12-A285762(n-3)) + A285762(n-12-A285762(n-12)): fi: end:
%Y Cf. A005185, A063882, A285757, A285758, A285759, A285760, A285761.
%K nonn
%O 1,2
%A _Nathan Fox_, Apr 25 2017
|
