cp's OEIS Frontend

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.

%I A072557 #10 Aug 25 2015 16:35:12
%S A072557 5,11,16,17,18,23,29,34,35,36,41,47,52,53,54,59,65,70,71,72,77,83,88,
%T A072557 89,90,95,101,106,107,108,113,119,124,125,126,131,137,142,143,144,149,
%U A072557 155,160,161,162,167,173,178,179,180,185,191,196,197,198,203,209,214
%N 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.
%C A072557 Denominators of w(k) are = 1,3 or 9 only.
%H A072557 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 1, -1).
%F A072557 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.
%e A072557 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
%t A072557 LinearRecurrence[{1, 0, 0, 0, 1, -1},{5, 11, 16, 17, 18, 23},58] (* _Ray Chandler_, Aug 25 2015 *)
%Y A072557 Cf. A072560, A072561.
%K A072557 nonn
%O A072557 1,1
%A A072557 _Benoit Cloitre_, Aug 06 2002