cp's OEIS Frontend

A284053 Relative of Hofstadter Q-sequence.

%I A284053 #14 Nov 22 2021 10:14:34
%S A284053 9,20,5,5,20,9,20,5,5,20,9,5,10,10,20,9,5,15,15,40,9,10,20,15,40,9,15,
%T A284053 25,15,40,9,20,25,15,60,9,25,25,20,60,9,25,30,25,60,9,25,40,20,60,9,
%U A284053 30,45,20,80,9,40,35,30,80,9,45,35,30,100,9,35,55,25,80,9,35,55,35,100
%N A284053 Relative of Hofstadter Q-sequence.
%C A284053 This sequence is defined by a(n) = 0 for n <= 0; a(1) = 9, a(2) = 20, a(3) = 5, a(4) = 5, a(5) = 20, a(6) = 9, a(7) = 20, a(8) = 5, a(9) = 5, a(10) = 20, a(11) = 9, a(12) = 5, a(13) = 10, a(14) = 10, a(15) = 20; thereafter a(n) = a(n-a(n-1)) + a(n-a(n-2)).
%C A284053 Similar to Hofstadter's Q-sequence A005185 but with different starting values.
%C A284053 Much like the Hofstadter Q-sequence A005185, it is not known if this sequence is defined for all positive n.
%C A284053 This sequence has a similar structure to A272610. That sequence consists of five interleaved sequences: four chaotic sequences and a sequence of all 4's. This sequence also consists of five interleaved sequences: four chaotic sequences and a sequence of all 9's.
%C A284053 If the 20's in the initial condition are each replaced by larger numbers, the general structure of this sequence does not change.
%H A284053 Nathan Fox, <a href="/A284053/b284053.txt">Table of n, a(n) for n = 1..10000</a>
%p A284053 A284053:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 9: elif n = 2 then 20: elif n = 3 then 5: elif n = 4 then 5: elif n = 5 then 20: elif n = 6 then 9: elif n = 7 then 20: elif n = 8 then 5: elif n = 9 then 5: elif n = 10 then 20: elif n = 11 then 9: elif n = 12 then 5: elif n = 13 then 10: elif n = 14 then 10: elif n = 15 then 20: else A284053(n-A284053(n-1)) + A284053(n-A284053(n-2)): fi: end:
%o A284053 (Python)
%o A284053 from functools import cache
%o A284053 @cache
%o A284053 def a(n):
%o A284053     if n <= 0: return 0
%o A284053     if n < 16:
%o A284053         return [9, 20, 5, 5, 20, 9, 20, 5, 5, 20, 9, 5, 10, 10, 20][n-1]
%o A284053     return a(n - a(n-1)) + a(n - a(n-2))
%o A284053 print([a(n) for n in range(1, 76)]) # _Michael S. Branicky_, Sep 20 2021
%Y A284053 Cf. A005185, A272610, A283903, A284054.
%K A284053 nonn
%O A284053 1,1
%A A284053 _Nathan Fox_, Mar 19 2017