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A284383 a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 2; a(n) is the largest composite number <= (a(n-a(n-1)) + a(n-a(n-2))) for n > 4.

%I A284383 #19 Mar 30 2017 01:14:36
%S A284383 1,2,3,2,4,4,6,4,6,6,8,6,10,6,10,10,12,8,14,10,14,10,16,10,16,16,16,
%T A284383 12,22,12,20,16,22,14,24,16,24,16,26,16,26,26,24,18,30,22,28,26,30,20,
%U A284383 34,24,36,20,38,24,36,24,40,26,38,26,40,26,42,26,42,42,32,28,50,28,46,34
%N A284383 a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 2; a(n) is the largest composite number <= (a(n-a(n-1)) + a(n-a(n-2))) for n > 4.
%H A284383 Altug Alkan, <a href="/A284383/b284383.txt">Table of n, a(n) for n = 1..10000</a>
%H A284383 Altug Alkan, <a href="/A284383/a284383.png">Alternative scatterplot of A284383</a>
%H A284383 Altug Alkan, <a href="/A284383/a284383_1.png">Illustration for A284383</a>
%F A284383 a(1) = 1, a(2) = 2, a(3) = 3; a(n) = a(n-a(n-1)) + a(n-a(n-2)) - A010051(a(n-a(n-1)) + a(n-a(n-2))) for n > 3.
%e A284383 a(5) = 4 because a(5 - a(4)) + a(5 - a(3)) = a(3) + a(2) = 3 + 2 = 5 and largest composite number <= 5 is 4.
%t A284383 a[n_] := a[n] = If[n <= 4, n - 2 Boole[n == 4], k = 0; While[! CompositeQ@ Set[m, a[n - a[n - 1]] + a[n - a[n - 2]] - k], k++]; m]; Array[a, 74] (* _Michael De Vlieger_, Mar 29 2017 *)
%o A284383 (PARI) f(n) = n-isprime(n);
%o A284383 a=vector(1000); a[1]=1;a[2]=2;a[3]=3; for(n=4, #a, a[n] = f(a[n-a[n-1]]+a[n-a[n-2]])); a
%Y A284383 Cf. A005185, A010051, A014684, A113523, A284374.
%K A284383 nonn
%O A284383 1,2
%A A284383 _Altug Alkan_, Mar 26 2017