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

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, 95, 51, 41, 21, 19, 39, 89, 119, 135, 73, 59, 113, 143, 161, 171, 181, 187, 3, 101, 39, 131, 179, 51, 71, 155, 99, 175, 27, 145, 207, 239, 129, 205, 61, 177, 121, 27, 85, 201, 133

Offset: 0

Author

Zak Seidov, Nov 18 2005

Keywords

• nonn

Comments

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.

Examples

			prime(1)=2, hence a(1) = (0 + 2)/2^1 = 1;
prime(2)=3, hence a(2) = (a(1)+3)/2^2 = 1;
prime(3)=5, hence a(3) = (a(2)+5)/2^1 = 3;
prime(4)=7, hence a(4) = (a(3)+7)/2^1 = 5, etc.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• Jesse Sealand, Project to manage derivative sequences.

Crossrefs

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

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

Programs

Maple

N:= 1000: # to get N terms
T:= 0; A[0]:= T;
for n from 1 to N do
   T:= T + ithprime(n);
   T:= T / 2^padic[ordp](T,2);
   A[n]:= T;
od:
seq(A[n],n=0..N); # Robert Israel, Jun 01 2014

Mathematica

Do[{
  If[n == 1, t = 0];
  t = Prime[n] + t;
  k = IntegerExponent[t, 2];
  t = t/(Power[2, k ]);
  (* a(n)=t *)
  }, {n, 1, 1000}]
(* Jesse Sealand, Aug 17 2019 *)

Extensions

Definition corrected and offset changed by N. J. A. Sloane, Sep 01 2019.