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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 24 02:56 EDT 2021. Contains 345415 sequences. (Running on oeis4.)