A072557 Let w(n) be defined by the following recurrence: w(1)=w(2)=w(3)=1, w(n)=(w(n-1)*w(n-2)+(w(n-1)+w(n-2))/3) / w(n-3); sequence gives values of n such that w(n) is an integer.

5, 11, 16, 17, 18, 23, 29, 34, 35, 36, 41, 47, 52, 53, 54, 59, 65, 70, 71, 72, 77, 83, 88, 89, 90, 95, 101, 106, 107, 108, 113, 119, 124, 125, 126, 131, 137, 142, 143, 144, 149, 155, 160, 161, 162, 167, 173, 178, 179, 180, 185, 191, 196, 197, 198, 203, 209, 214

Offset

1,1

Comments

Denominators of w(k) are = 1,3 or 9 only.

Links

Table of n, a(n) for n=1..58.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 1, -1).

Formula

lim n -> infinity a(n)/n = 18/5. sequence contains numbers of form (5+18k), (11+18k), (16+18k), (17+18k), (18+18k) k>=0.

Example

First 11 values of w(n) are 5/3, 23/9, 17/3, 31/3, 25, 143/3, 353/3, 2039/9, 1685/3, 3251/3, 2689 which are integers for k= 5 and 11 hence a(1)=5 a(2)=11

Mathematica

LinearRecurrence[{1, 0, 0, 0, 1, -1}, {5, 11, 16, 17, 18, 23}, 58] (* Ray Chandler, Aug 25 2015 *)

Crossrefs

Cf. A072560, A072561.

Sequence in context: A259067 A314080 A337947 * A324076 A314081 A314082

Adjacent sequences: A072554 A072555 A072556 * A072558 A072559 A072560

Keyword

nonn

Author

Benoit Cloitre, Aug 06 2002

Status

approved