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A305557 a(1) = a(2) = 1; a(n) = n - a(a(n-2)) - a(n-a(n-2)) for n > 2.

%I A305557 #18 Jun 26 2018 13:08:43
%S A305557 1,1,1,2,2,3,4,5,5,6,6,6,6,6,7,7,7,8,9,9,10,11,11,12,13,14,15,16,16,
%T A305557 17,17,18,19,19,19,20,20,21,21,21,22,22,22,22,23,23,24,24,24,24,24,24,
%U A305557 25,25,25,26,26,26,26,27,28,28,28,28,29,29,30,31,31,32,33,33,33,33,34,35,36,37,37
%N A305557 a(1) = a(2) = 1; a(n) = n - a(a(n-2)) - a(n-a(n-2)) for n > 2.
%C A305557 Let a_i(n) = n - a_i(a_i(n-i)) - a_i(n-a_i(n-i)). This sequence is generated by a_2(n) with initial conditions 1, 1.
%H A305557 Altug Alkan, <a href="/A305557/a305557.pdf">Proof of basic property</a>
%F A305557 a(n+1) - a(n) = 0 or 1 for all n >= 1 and a(n) hits every positive integer.
%p A305557 a:=proc(n) option remember: if n<3 then 1 else n-procname(procname(n-2))-procname(n-procname(n-2)) fi; end: seq(a(n), n=1..100); # _Muniru A Asiru_, Jun 26 2018
%o A305557 (PARI) a=vector(99); a[1]=a[2]=1; for(n=3, #a, a[n] = n-a[a[n-2]]-a[n-a[n-2]]); a
%o A305557 (GAP) a:=[1,1];; for n in [3..100] do a[n]:=n-a[a[n-2]]-a[n-a[n-2]]; od; a; # _Muniru A Asiru_, Jun 26 2018
%Y A305557 Cf. A005229, A287422, A305845.
%K A305557 nonn,easy
%O A305557 1,4
%A A305557 _Altug Alkan_, Jun 21 2018