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A110365 a(1)=2, a(n+1) = a(n)*A010888(a(n)).

%I A110365 #16 Mar 17 2019 11:23:10
%S A110365 2,4,16,112,448,3136,12544,87808,351232,2458624,9834496,68841472,
%T A110365 275365888,1927561216,7710244864,53971714048,215886856192,
%U A110365 1511207993344,6044831973376,42313823813632,169255295254528,1184787066781696,4739148267126784,33174037869887488
%N A110365 a(1)=2, a(n+1) = a(n)*A010888(a(n)).
%C A110365 From a(2) onwards, the digital root follows the pattern alternately 4,7,4,7,4,7,...
%H A110365 Colin Barker, <a href="/A110365/b110365.txt">Table of n, a(n) for n = 1..1000</a>
%H A110365 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,28).
%F A110365 a(1) = 2, a(2) = 4, a(3) = 16. a(2*n) = 4*a(2*n-1), a(2*n+1) = 7*a(2*n) for n > 1.
%F A110365 From _Colin Barker_, May 05 2016: (Start)
%F A110365 a(n) = 2^(-1+n)*(7^(1/2*(-3+n))*(2-2*(-1)^n + sqrt(7) + (-1)^n*sqrt(7))) for n > 1.
%F A110365 a(n) = 2^n*7^(n/2-1) for n > 1 and even.
%F A110365 a(n) = 2^(n+1)*7^((n-3)/2) for n > 1 and odd.
%F A110365 a(n) = 28*a(n-2) for n > 3.
%F A110365 G.f.: 2*x*(1+2*x-20*x^2) / (1-28*x^2).
%F A110365 (End)
%F A110365 E.g.f.: (-7 + 70*x + 7*cosh(2*Sqrt(7)*x) + 2*sqrt(7)*sinh(2*sqrt(7)*x))/49. - _Ilya Gutkovskiy_, May 05 2016
%t A110365 k = 2; Do[Print[k]; k *= Mod[Plus @@ IntegerDigits[k], 9], {n, 1, 30}] (* _Ryan Propper_, Oct 13 2005 *)
%t A110365 LinearRecurrence[{0,28},{2,4,16},30] (* _Harvey P. Dale_, Mar 17 2019 *)
%o A110365 (PARI) Vec(2*x*(1+2*x-20*x^2)/(1-28*x^2) + O(x^50)) \\ _Colin Barker_, May 05 2016
%Y A110365 Cf. A010888, A047892.
%K A110365 base,easy,nonn
%O A110365 1,1
%A A110365 _Amarnath Murthy_, Jul 24 2005
%E A110365 More terms from _Ryan Propper_, Oct 13 2005
%E A110365 Name clarified by _Robert Israel_, May 05 2016