login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A175409 Successive numbers of consecutive positive terms to add when rearranging the alternating harmonic series to sum to log[7/3]. 0
1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Let s = log(7/3). Add a(n) positive terms 1 + 1/3 + 1/5 + ... + 1/(2a(n)-1)until their sum is greater than s, then subtract negative terms 1/2, 1/4, ... until the sum drops below s. Continue alternating in this way, adding a(2) consecutive positive terms, subtracting negative terms, and so on. The numbers a(n) are the terms of the sequence.
Since x = (1/4)exp(2s) = 49/36 is rational, a result in the reference shows that this sequence is eventually periodic.
REFERENCES
Mohammad K. Azarian, Problem 1218, Pi Mu Epsilon Journal, Vol. 13, No. 2, Spring 2010, p. 116. Solution published in Vol. 13, No. 3, Fall 2010, pp. 183-185.
LINKS
Francisco J. Freniche, On Riemann's Rearrangement Theorem for the Alternating Harmonic Series, Amer. Math. Monthly 117(2010), 442-448.
EXAMPLE
s = log(7/3) = 0.847298. The first term, 1, of the alternating harmonic series already exceeds s, so a(1)=1. Subtracting negative terms, we get 1-1/2 = 1/2, which is less than s. Then, adding 1/3 gives 0.833333, which is less than s, so we also add a second term, 1/5, to get 1.03333 which exceeds s. Thus a(2)=2.
CROSSREFS
Sequence in context: A161113 A161048 A152830 * A161073 A161112 A161047
KEYWORD
nonn
AUTHOR
John W. Layman, May 04 2010
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)