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A297996 a(1)=2, a(2)=3, a(3)=5 and a(n) = (a(1) + a(2) + a(3) + ... + a(n-1))/a(n-1).

%I A297996 #23 Dec 31 2021 14:36:10
%S A297996 2,3,5,2,6,3,7,4,8,5,9,6,10,7,11,8,12,9,13,10,14,11,15,12,16,13,17,14,
%T A297996 18,15,19,16,20,17,21,18,22,19,23,20,24,21,25,22,26,23,27,24,28,25,29,
%U A297996 26,30,27,31,28,32,29,33,30,34,31,35,32,36,33,37,34,38,35
%N A297996 a(1)=2, a(2)=3, a(3)=5 and a(n) = (a(1) + a(2) + a(3) + ... + a(n-1))/a(n-1).
%H A297996 Colin Barker, <a href="/A297996/b297996.txt">Table of n, a(n) for n = 1..1000</a>
%H A297996 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A297996 a(n) = A168230(n+1) for n >= 3.
%F A297996 From _Colin Barker_, Jan 29 2018: (Start)
%F A297996 G.f.: x*(2 + x - 4*x^3 + 2*x^4) / ((1 - x)^2*(1 + x)).
%F A297996 a(n) = n/2 for n>2 and even.
%F A297996 a(n) = (n+7)/2 for n>2 and odd.
%F A297996 a(n) = a(n-1) + a(n-2) - a(n-3) for n>5.
%F A297996 (End)
%t A297996 Nest[Append[#, Total[#]/Last[#]] &, Prime@ Range@ 3, 67] (* _Michael De Vlieger_, Jan 10 2018 *)
%t A297996 LinearRecurrence[{1,1,-1},{2,3,5,2,6},70] (* _Harvey P. Dale_, Dec 31 2021 *)
%o A297996 (PARI) lista(nn) = {va = vector(nn); for (n=1, 3, va[n] = prime(n)); for (n=4, nn, va[n] = sum(k=1, n-1, va[k])/va[n-1];); va;} \\ _Michel Marcus_, Jan 10 2018
%o A297996 (PARI) Vec(x*(2 + x - 4*x^3 + 2*x^4) / ((1 - x)^2*(1 + x)) + O(x^100)) \\ _Colin Barker_, Jan 29 2018
%Y A297996 Cf. A168230.
%K A297996 nonn,easy,less
%O A297996 1,1
%A A297996 _Mateusz Pasternak_, Jan 10 2018
%E A297996 More terms from _Michel Marcus_, Jan 10 2018