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
Keywords
Examples
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
Links
- Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 1, -1).
Programs
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Mathematica
LinearRecurrence[{1, 0, 0, 0, 1, -1},{5, 11, 16, 17, 18, 23},58] (* Ray Chandler, Aug 25 2015 *)
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.
Comments