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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
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 * A337128 A208509 A086233
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 April 23 07:16 EDT 2024. Contains 371905 sequences. (Running on oeis4.)