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A287422 a(1) = a(2) = 1; a(n) = n - a(a(n-1)) - a(n-a(n-1)) for n > 2.

%I A287422 #36 Sep 08 2022 08:46:19
%S A287422 1,1,1,2,3,4,4,4,4,4,5,5,6,6,7,8,9,10,11,11,12,13,13,13,14,15,15,15,
%T A287422 16,16,16,16,16,16,16,17,17,17,17,18,18,19,19,19,19,20,21,21,22,22,22,
%U A287422 23,24,25,25,26,26,27,28,29,29,30,31,32,33,34,35,36,36,37,38,39,40,40,41,42,42,42,43,44,45,46,46
%N A287422 a(1) = a(2) = 1; a(n) = n - a(a(n-1)) - a(n-a(n-1)) for n > 2.
%H A287422 Michael De Vlieger, <a href="/A287422/b287422.txt">Table of n, a(n) for n = 1..10000</a>
%H A287422 Altug Alkan, <a href="/A287422/a287422.png">Plot of a(n)-n/2 for n<=2^20</a>
%H A287422 Altug Alkan, <a href="/A287422/a287422_1.png">Plot of (a(n-a(n-1))/n, a(a(n-1))/n) for n <= 250000</a>
%H A287422 Rémy Sigrist, <a href="/A287422/a287422_2.png">Colored scatterplot of (a(n-a(n-1))/n, a(a(n-1))/n) for n <= 100000000</a> (where the hue is function of n)
%t A287422 Nest[Function[{a, n}, Append[a, n - a[[a[[-1]] ]] - a[[-a[[-1]] ]] ] ] @@ {#, Length@ # + 1} &, {1, 1}, 80] (* _Michael De Vlieger_, Aug 07 2018 *)
%o A287422 (PARI) q=vector(10000); q[1]=q[2]=1; for(n=3, #q, q[n]=n-q[q[n-1]]-q[n-q[n-1]]); q
%o A287422 (Magma) I:=[1,1,1,2]; [n le 4 select I[n] else n - Self(Self(n-1)) - Self(n-Self(n-1)): n in [1..100]]; // _Vincenzo Librandi_, Aug 08 2018
%Y A287422 Cf. A003160, A004001, A005206, A088462, A189663.
%K A287422 nonn
%O A287422 1,4
%A A287422 _Altug Alkan_, Jun 24 2017