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
Keywords
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
Programs
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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
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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.
Comments