A303219 - OEIS

%I #74 Sep 08 2022 08:46:21

%S 1,2,3,4,5,6,7,8,9,10,11,12,12,12,13,14,15,16,17,18,18,18,19,20,21,22,

%T 23,24,24,24,25,26,27,28,29,30,30,30,31,32,33,34,34,34,35,36,36,36,37,

%U 38,39,40,41,42,42,42,43,44,45,46,47,48,48,48,49,50,51,52,52,52,53,54,54,54,55,56

%N a(n) = n for n <= 11. Thereafter a(n) = a(n-a(n-2)) + a(n-a(n-4)) + a(n-a(n-6)).

%C Let a_i(n) = n for n <= 6*i - 1. Thereafter a_i(n) = a_i(n-a_i(n-i)) + a_i(n-a_i(n-2*i)) + a_i(n-a_i(n-3*i)). This sequence is a_2(n).

%H Altug Alkan, <a href="/A303219/b303219.txt">Table of n, a(n) for n = 1..10000</a>

%H 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.

%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

%t nmax = 100;

%t q[_] = 0; For[n = 1, n <= 11, n++, q[n] = n]; For[n = 12, n <= nmax, n++, q[n] = q[n - q[n-2]] + q[n - q[n-4]] + q[n - q[n-6]]]; Array[q, nmax] (* _Jean-François Alcover_, Feb 18 2019, from PARI *)

%o (PARI) q=vector(100); for(n=1, 11, q[n]=n);for(n=12, #q, q[n] = q[n-q[n-2]] + q[n-q[n-4]] + q[n-q[n-6]]); q

%o (GAP) a:=List([1..11],i->i);; for n in [12..100] do a[n]:=a[n-a[n-2]]+a[n-a[n-4]]+a[n-a[n-6]]; od; a; # _Muniru A Asiru_, May 19 2018

%o (Magma)  [n le 11 select n else Self(n-Self(n-2))+Self(n-Self(n-4))+Self(n-Self(n-6)): n in [1..70]]; // _Vincenzo Librandi_, May 20 2018

%Y Cf. A278055.

%K nonn

%O 1,2

%A _Altug Alkan_, May 17 2018