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A114216 a(0)=0; thereafter a(n) = largest odd divisor of a(n-1) + prime(n).

%I A114216 #43 Sep 01 2019 10:40:24
%S A114216 0,1,1,3,5,1,7,3,11,17,23,27,1,21,1,3,7,33,47,57,1,37,29,7,3,25,63,83,
%T A114216 95,51,41,21,19,39,89,119,135,73,59,113,143,161,171,181,187,3,101,39,
%U A114216 131,179,51,71,155,99,175,27,145,207,239,129,205,61,177,121,27,85,201,133
%N A114216 a(0)=0; thereafter a(n) =  largest odd divisor of a(n-1) + prime(n).
%C A114216 a(33899) = 123729 and the 33900th prime is 400559, hence 123729 + 400559 = 524288 = 2^19 and a(33900) = 1. Is a(33900) the last term equal to 1? No other terms with a(n) = 1 for n < 10000000.
%H A114216 Robert Israel, <a href="/A114216/b114216.txt">Table of n, a(n) for n = 0..10000</a>
%H A114216 Jesse Sealand, <a href="https://github.com/jessesealand/oeis-A114216-derivatives">Project to manage derivative sequences</a>.
%e A114216 prime(1)=2, hence a(1) = (0 + 2)/2^1 = 1;
%e A114216 prime(2)=3, hence a(2) = (a(1)+3)/2^2 = 1;
%e A114216 prime(3)=5, hence a(3) = (a(2)+5)/2^1 = 3;
%e A114216 prime(4)=7, hence a(4) = (a(3)+7)/2^1 = 5, etc.
%p A114216 N:= 1000: # to get N terms
%p A114216 T:= 0; A[0]:= T;
%p A114216 for n from 1 to N do
%p A114216    T:= T + ithprime(n);
%p A114216    T:= T / 2^padic[ordp](T,2);
%p A114216    A[n]:= T;
%p A114216 od:
%p A114216 seq(A[n],n=0..N); # _Robert Israel_, Jun 01 2014
%t A114216 Do[{
%t A114216   If[n == 1, t = 0];
%t A114216   t = Prime[n] + t;
%t A114216   k = IntegerExponent[t, 2];
%t A114216   t = t/(Power[2, k ]);
%t A114216   (* a(n)=t *)
%t A114216   }, {n, 1, 1000}]
%t A114216 (* _Jesse Sealand_, Aug 17 2019 *)
%Y A114216 Cf. A114217 (a(n)=1), A114221 (a(n)=3), A114222 (a(n)=7), A114223 (a(n)=11), A114224 (a(n)=17).
%Y A114216 Cf. A114218 lists the values of k for n with a(n)=1.
%K A114216 nonn
%O A114216 0,4
%A A114216 _Zak Seidov_, Nov 18 2005
%E A114216 Definition corrected and offset changed by _N. J. A. Sloane_, Sep 01 2019.