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.

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, 12, 22, 12, 20, 16, 22, 14, 24, 16, 24, 16, 26, 16, 26, 26, 24, 18, 30, 22, 28, 26, 30, 20, 34, 24, 36, 20, 38, 24, 36, 24, 40, 26, 38, 26, 40, 26, 42, 26, 42, 42, 32, 28, 50, 28, 46, 34

Offset: 1

Author

Altug Alkan, Mar 26 2017

Keywords

• nonn

Examples

			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.
		

Links

• Altug Alkan, Table of n, a(n) for n = 1..10000
• Altug Alkan, Alternative scatterplot of A284383
• Altug Alkan, Illustration for A284383

Crossrefs

Cf. A005185, A010051, A014684, A113523, A284374.

Programs

Mathematica

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 *)

PARI

f(n) = n-isprime(n);
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

Formula

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.