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a(0)=0; thereafter a(n) = largest odd divisor of a(n-1) + prime(n).
8

%I #43 Sep 01 2019 10:40:24

%S 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 95,51,41,21,19,39,89,119,135,73,59,113,143,161,171,181,187,3,101,39,

%U 131,179,51,71,155,99,175,27,145,207,239,129,205,61,177,121,27,85,201,133

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

%C 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 Robert Israel, <a href="/A114216/b114216.txt">Table of n, a(n) for n = 0..10000</a>

%H Jesse Sealand, <a href="https://github.com/jessesealand/oeis-A114216-derivatives">Project to manage derivative sequences</a>.

%e prime(1)=2, hence a(1) = (0 + 2)/2^1 = 1;

%e prime(2)=3, hence a(2) = (a(1)+3)/2^2 = 1;

%e prime(3)=5, hence a(3) = (a(2)+5)/2^1 = 3;

%e prime(4)=7, hence a(4) = (a(3)+7)/2^1 = 5, etc.

%p N:= 1000: # to get N terms

%p T:= 0; A[0]:= T;

%p for n from 1 to N do

%p T:= T + ithprime(n);

%p T:= T / 2^padic[ordp](T,2);

%p A[n]:= T;

%p od:

%p seq(A[n],n=0..N); # _Robert Israel_, Jun 01 2014

%t Do[{

%t If[n == 1, t = 0];

%t t = Prime[n] + t;

%t k = IntegerExponent[t, 2];

%t t = t/(Power[2, k ]);

%t (* a(n)=t *)

%t }, {n, 1, 1000}]

%t (* _Jesse Sealand_, Aug 17 2019 *)

%Y Cf. A114217 (a(n)=1), A114221 (a(n)=3), A114222 (a(n)=7), A114223 (a(n)=11), A114224 (a(n)=17).

%Y Cf. A114218 lists the values of k for n with a(n)=1.

%K nonn

%O 0,4

%A _Zak Seidov_, Nov 18 2005

%E Definition corrected and offset changed by _N. J. A. Sloane_, Sep 01 2019.