cp's OEIS Frontend

A278055 Relative of Hofstadter Q-sequence: a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 4, a(5) = 5; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 5.

%I A278055 #21 Dec 02 2016 23:02:54
%S A278055 1,2,3,4,5,6,6,7,8,9,9,10,11,12,12,13,14,15,15,16,17,17,18,18,19,20,
%T A278055 21,21,22,23,24,24,25,26,26,27,27,28,29,30,30,31,32,33,33,34,35,35,36,
%U A278055 36,37,38,39,39,40,41,42,42,43,44,44,45,45,46,47,48,48,49,50,50,51
%N A278055 Relative of Hofstadter Q-sequence: a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 4, a(5) = 5; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 5.
%C A278055 This sequence is monotonic, with successive terms increasing by 0 or 1. So the sequence hits every positive integer.
%C A278055 A number k appears twice in this sequence if and only if for some i, k is congruent to A057198(i) mod 3^i and k > A057198(i).
%H A278055 Nathan Fox, <a href="/A278055/b278055.txt">Table of n, a(n) for n = 1..10000</a>
%H A278055 Nathan Fox, <a href="https://arxiv.org/abs/1611.08244">A Slow Relative of Hofstadter's Q-Sequence</a>, arXiv preprint arXiv:1611.08244 [math.NT], 2016.
%F A278055 a(n) ~ 2n/3.
%t A278055 a[n_] := a[n] = a[n - a[n -1]] + a[n - a[n -2]] + a[n - a[n -3]]; a[1] = 1; a[2] = 2; a[3] = 3; a[4] = 4; a[5] = 5; Array[a, 71] (* _Robert G. Wilson v_, Dec 02 2016 *)
%o A278055 (PARI) A=Vecsmall([]);
%o A278055 a(n)=if(n<7, return(n)); if(#A<n, A=concat(A,vectorsmall(n-#A)), if(A[n], return(A[n]))); A[n]=a(n-a(n-3)) + a(n-a(n-2)) + a(n-a(n-1)) \\ _Charles R Greathouse IV_, Nov 19 2016
%Y A278055 Cf. A005185, A057198, A063882, A267501, A274058.
%K A278055 nonn
%O A278055 1,2
%A A278055 _Nathan Fox_, Nov 10 2016