A285509 a(1) = 1; a(2) = a(3) = a(4) = 2; a(n) = a(a(n-1)-1) + a(n-a(n-3)) for n > 4.

1, 2, 2, 2, 3, 4, 5, 5, 5, 5, 6, 8, 10, 10, 10, 9, 10, 10, 10, 10, 11, 13, 18, 20, 18, 15, 15, 15, 20, 20, 19, 18, 20, 20, 20, 19, 20, 20, 20, 20, 21, 23, 31, 38, 33, 28, 20, 20, 21, 30, 39, 39, 38, 30, 29, 25, 35, 40, 40, 38, 31, 33, 36, 40, 38, 40, 35, 40, 40, 40, 39, 38, 40, 40, 40, 39, 40, 40, 40, 40, 41, 43, 54, 69

Offset: 1

Author

Altug Alkan, Apr 20 2017

Keywords

• nonn
• look

Comments

Although sequence is unpredictable with its complex growth characteristic and generational structure, it has various signs of order and there are many temporary and simple patterns on it. For example, values of a(n) such that a(n) = a(n + 1) = a(n + 2) = a(n + 3) are 5, 10, 20, 40, 80, 160, 320, 640, 1280, ...

Examples

			a(5) = 3 because a(5) = a(a(4)-1) + a(5-a(2)) = a(1) + a(3) = 2.
		

Links

• Altug Alkan, Table of n, a(n) for n = 1..10000
• Altug Alkan, Alternative scatterplot of A285509

Crossrefs

Cf. A005185, A055748, A284523, A285507

Programs

Mathematica

a[1]=1; a[2]=a[3]=a[4]=2; a[n_] := a[n] = a[a[n-1]-1] + a[n-a[n-3]]; Array[a, 84] (* Giovanni Resta, Apr 21 2017 *)

PARI

a=vector(10000); a[1]=1;a[2]=a[3]=a[4]=2; for(n=5, #a, a[n]=a[a[n-1]-1]+a[n-a[n-3]]); va = vector(10000, n, a[n])