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

1,2

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, ...

Links

Altug Alkan, Table of n, a(n) for n = 1..10000

Altug Alkan, Alternative scatterplot of A285509

Example

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

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 *)

Prog

(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])

Crossrefs

Cf. A005185, A055748, A284523, A285507

Sequence in context: A323259 A330918 A162352 * A194813 A096533 A230413

Adjacent sequences: A285506 A285507 A285508 * A285510 A285511 A285512

Keyword

nonn,look

Author

Altug Alkan, Apr 20 2017

Status

approved