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A114216 a(0)=0; thereafter a(n) =  largest odd divisor of a(n-1) + prime(n). 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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.

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

Jesse Sealand, Project to manage derivative sequences.

EXAMPLE

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.

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 *)

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.

Sequence in context: A158858 A202356 A152204 * A208509 A086233 A318190

Adjacent sequences:  A114213 A114214 A114215 * A114217 A114218 A114219

KEYWORD

nonn

AUTHOR

Zak Seidov, Nov 18 2005

EXTENSIONS

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

STATUS

approved

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Last modified October 23 23:51 EDT 2019. Contains 328379 sequences. (Running on oeis4.)