Talk:Kempner function

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 Field:  Number theory
This Wikipedia article is created by PlanetMath editor, who created the original entry on the topic at PlanetMath.


Now all the Smarandache constants from 1 to 16 are latex typeset in the article. Please improve the article, but do not blank portions of it. Your cooperativity is appreciated. Danko Georgiev MD 02:24, 11 May 2007 (UTC)

It would be appreciated if you placed the full name of the authors of the articles, rather than Name I. That is considered a depreciated style in Wikipedia. I fixed most of your other articles, but I don't have adequate information to do it here. Alternatively, remove the initials entirely. — Arthur Rubin | (talk) 06:19, 16 May 2007 (UTC)
Thank you for comments, however this is the preferred reference style by me and follows the guidelines of PubMed. I am not aware whether in mathematics this is bad style to provide refs, but as I have provided DOI clickable links at all places where possible, I don't think my ref style is bad. I prefer to edit something with meaning, and although I conform my articles to the PubMed ref style, I have no time to re-edit the refs. Please appologize me for that, there are Wikipedians that are spell-checkers, etc., so some person who is interested to repair the ref style of articles is free to do it. I don't mind this :-) Danko Georgiev MD 07:18, 17 May 2007 (UTC)
The original wikipedia page seems to have been copied and pasted practically unchanged from MathWorld by a lazy editor. As a result the conventions used for references there are what appear here. The only contribution of the original editor seems to have been to add faulty links to Smarandache's Notions Journal on Smarandache's home page. They appear as SNJX.pdf rather than SFJX.pdf on Smarandache's home page. I have therefore removed these faulty links. Any person who is interested in providing correct links may do so. I don't mind this ;-) I hope such a person will find the time to do so. --Mathsci 22:44, 5 June 2007 (UTC)
I am the "lazy editor" both on Wikipedia and PlanetMath see my user page. I have replied in detail at MathSci's talk page. Danko Georgiev MD 13:05, 6 June 2007 (UTC)

Proposal to remove some material on Smarandache constants[edit]

I propose that the material on convergent series related to S(n) be considerably shortened or removed altogether. It could be replaced by a short description of one or two representative results, possibly with a corresponding result for the pseudo-Smarandache function. Taken as a whole, the sixteen constants of Samarandache are arbitrary and seem to be quite unremarkable. They do not seem to merit the disproportionate amount of space devoted to them. (In addition some errors seem to have been introduced during the transfer from MathWorld articles or the orginal primary sources.) --Mathsci 19:00, 26 July 2007 (UTC)

I have made the proposed changes, including Richard Pinch's result on the convergence of the series for Z(n). If you object to these changes, please discuss them on this talk page. Throughout its history S(n) has appeared in recreational problems, often of an advanced nature, but sometimes trivial; we don't need to list all these problems on WP. --Mathsci 06:17, 27 July 2007 (UTC)

almost all[edit]

The article says

... Paul Erdos pointed out that for almost all n the function S(n) coincides with the largest prime factor of n.

Unfortunately it's not clear from context what "almost all" means. It could mean "with only finitely many exceptions" (that's probably the most available reading, but intuitively it seems unlikely; if there are exceptions I'd expect infinitely many). Or, it could mean that the set of exceptions has asymptotic density zero. Or it could mean something else. Can anyone clarify? --Trovatore 18:32, 5 August 2007 (UTC)

This is explained in the reference (it can be accessed through jstor). Erdos himself used the phrase "almost all". He then made this precise: the number of integers less than n for which the assertion is true, when divided by n, should tend to 1 as n tends to infinity. I suspect this is what you mean by asymptotic density. Pleae feel free to clarify this sentence ... without making it unreadable. --Mathsci 19:30, 5 August 2007 (UTC)


Is this really a notable function? Looking at the references, we see a number of publications associated with an apparent vanity press (Erhus University Press, which has no apparent web presence that I can find), a few website mentions, and a small handful of conference presentations or journal articles mentioning the topic (some of which are Smarandache's own toy journals). Three of these mentions are about previous discussions of the so-called Smarandache function — but the fact that this function was briefly discussed decades ago hardly adds to its notability.

So, here are the most interesting references (to my mind):

  • S. Tabirca, T. Tabirca, K. Reynolds, L.T. Yang (2004). "Calculating Smarandache function in parallel". Parallel and Distributed Computing, 2004. Third International Symposium on Algorithms, Models and Tools for Parallel Computing on Heterogeneous Networks,: pp.79–82.
  • Problem 6674 [1991 ,965], American Mathematical Monthly, 101 (1994), 179.

I haven't read the former, but it appears to me that it's using the function as a parallel calculation problem. That doesn't seem to make the function interesting. I don't know the latter either. Anyone have that issue handy?

The remainder of the references are either web articles, books by Erhus University Press, or articles in Smarandache journals.

So, is this really a notable function, or just another of those things discussed by Smarandache and a few of his entourage? Phiwum (talk) 15:33, 17 December 2009 (UTC)

To show its notability, I added the section "An application" on my proof that e is irrational. Note that my paper was published in the mainstream journal Amer. Math. Monthly and that Waldschmidt's lecture on it was given at the Arizona Winter School, which is not part of Smarandache's empire. Jsondow (talk) 03:38, 20 June 2010 (UTC)

The section "An application" has been deleted by Arthur Rubin, along with all my other recent edits. His reasons are "Almost all of the last change are wrong, have wrong links, unnecessarily change from wikilformat to math, or are misleading". I agree that changing from wikiformat to math is unnecessary. But the mathematics in "An application" and in my other edits was relevant and correct (he does not point out any math errors). I tried to revert to my version, but it seems that I cannot, because there is a more recent version than his. Rubin has thrown out the baby with the bathwater. Jsondow (talk) 14:38, 20 June 2010 (UTC)

My (almost) detailed commentary as to that last edit. I looked at each changed section. Each of the changes, other than to the added section, left the article less correct and/or readable than it had been before. The added section seems reasonable in concept, although you really shouldn't add references to your own paper, per WP:COI (which was not part of the reason for my revert). However, many (i.e., all that I checked) of the wikilinks were wrong or inappropriate, per Wikipedia guidelines. I should have a copy of the Monthly article around here somewhere; I'll see if I can put together an appropriate section. (Waldschmidt's lecture is almost certainly not a "reliable source", as we define it.)
As for me, I don't know why the function is considered notable; I suspect it's because Smarandache had been editor-in-chief of a few journals which have not been established to be WP:FRINGE. — Arthur Rubin (talk) 18:12, 20 June 2010 (UTC)

You explain your wholesale deletion of all my mathematical edits by saying that they "left the article less correct". (Earlier you said they "are wrong".) But again you do not give a single example of a mathematical error in them. Can you give one?

My article in the Monthly is available at the link in the reference you deleted. I look forward to seeing your version of the section you deleted. Jsondow (talk) 13:05, 21 June 2010 (UTC)

The notability of the function is shown in part by the application of it that you deleted, and by the two references to it which you also deleted. Jsondow (talk) 18:18, 21 June 2010 (UTC)

If you look closely, you'll see that I restored your edits (after unmathifying) except for your added section.
As for the added section, I don't see the notability of the Smarandache function even in your paper, and I can't say I'm impressed by the notability of your paper. Your paper is apparently accurate (although I would have preferred to read it from Jstor than from Arxiv), but I don't really see the notability.
You also have provided no evidence that the supporting reference from the 2008 Arizona Winter School was actually published.
You can copy your added section here to the talk page, for discussion, if you want to. I probably won't comment further, but you shouldn't comment here, either, because of WP:COI. — Arthur Rubin (talk) 21:27, 21 June 2010 (UTC)

Thank you for restoring my edits above the added-then-deleted section. A modified version of that section appears below (in imperfect wikiformat). For the benefit of readers without access to Jstor, I give both arXiv and Jstor links to reference #1. Even though it is not yet published, reference #2 is included for the benefit of mathematical readers.

An application

Like S(n), the number e can be defined in terms of factorials (see the infinite series in Alternative characterizations). This leads to a lower bound on the distance from e to any rational number, in terms of the Smarandache function: if p and q are any integers with q > 1, then [1]

In particular, ep/q. This gives a new proof that e is an irrational number. [2]

References and notes

1. Jonathan Sondow (2006). "A Geometric Proof that e Is Irrational and a New Measure of Its Irrationality". Amer. Math. Monthly 113: 637-641. (arXiv) (Jstor)
2. Michel Waldschmidt, "An Introduction to Irrationality and Transcendence Methods". 2008 Arizona Winter School. (Section 1.2.7 is an exposition of the proof and the Smarandache function.)

Jsondow (talk) 21:01, 22 June 2010 (UTC)

Concerns Regarding Naming and Attribution[edit]

The subject material of this article was first investigated in the 1880s and, as the article says, Florentin Smarandache named this after himself about a century later. Dr. Smarandache evidently has a sophisticated machinery for "auto-eponymous" promotion, as reported in a previous AfD. Echoing the above, there are many unpublished research papers on the "Smarandache function", e.g. here and here, but not a single published paper in the mainstream literature on this topic, according to WoS. Evidently, working mathematicians do not recognize this naming convention. Dr. Smarandache himself has only published a few low-citation papers the the peer-reviewed literature and none of them are on this topic. Although the naming has made some inroads, e.g. at MathWorld, there is no other real documentation. Rather, what the article uses for sources are a number of "papers" from Smarandache's own eponymous journals, i.e. the "Smarandache Function Journal" and the "Smarandache Notions Journal". Under the circumstances, it seems there should be serious concern regarding the naming and attribution – perhaps this should be relegated as redirect to a newly-named article? Thoughts? Thanks, Agricola44 (talk) 22:49, 12 June 2013 (UTC).

There has been no objection. I will perform the move. Note that the reference by "Ashbacher" is probably fraudulent. The book is self-published and does not acknowledge the long previous history (see Google Books). "Ashbacher" is likely to be Smarandache. Zaslav (talk) 16:40, 25 November 2013 (UTC)
Moved article to Kempner function, following the (well justified) name in (sequence A002034 in the OEIS).
Further remarks on "Charles Ashbacher": One of his books at Google Books Introduction to Neutrosophic Logic credits certain people with recommending the book for publication, one at "Texas State University, Arlington", which does not exist. I suspect "Ashbacher" is Smarandache and the other self-published books listed also are by Smarandache under pseudonyms. I found no evidence to contradict it, such as real mathematicians with the stated names. Other sources are in a journal Smarandache named for himself and should be considered suspicious. Zaslav (talk) 18:02, 25 November 2013 (UTC)
  • Thank you. I heartily concur with the renaming. Agricola44 (talk) 23:05, 25 November 2013 (UTC).

Why Kempner and not Lucas?[edit]

Why not calling it Lucas function? Since Lucas was the first not Kempner. — Preceding unsigned comment added by (talk) 13:38, 22 October 2014 (UTC)

Stigler's law of eponymy, presumably. —David Eppstein (talk) 17:46, 22 October 2014 (UTC)

Untrue paragraph[edit]

Thank you for your hard work. I often read wiki entries with great interest. I am not perfect, but I am not the worst person of the world either as some wikipedians portrait me. Unfortunately I saw much hostility and bias-ness against me in Wikipedia. If I committed mistakes, I apologize and I ask for forgiveness. I’ll not do in the future. Maybe because of some misunderstanding from both parts, between some supporters and some wikipedians, it brought me in this horrible situation. For example I was unfortunately named in Wikipedia “criminal,” “bank robber,” “suicide bomber,” etc. –- just too much exaggerations. But I forgave them and this misunderstanding has stopped long ago and I apologize for all that happened. There is nothing positive in wiki about me, only denigrations. I am not only bad, as this entry says, I have also many positive sides ( the readers should check the below site too, since I have the right to defense: ).

At History, in this entry, the paragraph about me is unfortunately malicious, biased and untrue. I proof this below.
1) “In 1980, following his habit, Florentin Smarandache re-named this function after himself.”

This assertion is untrue, since up to 1980 I had published very few research math papers only, and there was no notion at that time named after me. In 1979 I had barely graduated from my university. The paper was written in 1979 and submitted to a university journal. Its title was simply “A Function in the Number Theory”, not after my name. The function was much later named after me by my university professors Dr. Constantin Dumitrescu and Dr. Vasile Seleacu, in honor that I had graduated with the highest GPA among all my student colleagues.

2) “Several self-published and possibly pseudonymous books also used the same name…”.

This is also untrue. The books were published from several grants received by the above professors, and they are real persons (Dr. C. Dumitrescu and Dr. V. Seleacu – both from the University of Craiova, and Charles Ashbacher – American researcher), not pseudonyms. Charles Ashbacher is an author, editor, mathematician, computer programmer and sometimes adjunct instructor at Kirkwood Community College (Cedar Rapids, Iowa); see his site . See also his contact information in Iowa: and please call him to get convinced. People who brought positive things about my work were labelled sockpuppets in order to discourage or intimidate them unfortunately. Only negative things were left about me in wiki.

3) In 1979, when I wrote the paper “A Function in the Number Theory” in the communist Romania, I did not have access to old western journals to check my research, since we did not have much contact with western countries, as you know.
It happens in science that the same scientific result is discovered independently by different researchers. For example, L’Hospital’s Rule was discovered and proved by John Bernoulli in a letter sent to Guillaume L’Hospital.
4) References 7 is incorrect, since the book authors and the book title are: C. Dumitrescu and V. Seleacu, “The Smarandache Function”, not four authors and not that title.
5) Reference 8 is also inaccurate, since the book author is only Charles Ashbacher, not two authors.
I suffered for more than 10 years under this untrue stigma in Wikipedia. If I committed something wrong, politically, ideologically, etc. I apologize and I humbly feel that I was punished. I am a good American citizen and I love very much America.
I am now old and sick and I plan to retire.
So please let's reconcile. Please update this entry, and please let positive things about me to be added to other wiki entries (do not censor my name as a blacklisted person), and please remove those things that are untrue, or biased, or based on speculations. I do not want to fight with anybody. I appreciate your future fairness.
Wikipedia is a serious site, based on documentation, not on speculations. So, please correct the wrong paragraph about me.
(Florentin Smarandache) — Preceding unsigned comment added by FlSmarandache (talkcontribs) 18:59, 26 October 2014 (UTC)
Yes, you can try to give Charles Aschbacher a ring, but you'll be answered by Florentin pinching his nose. Also, Gallups still lists FS as professor, so his retirement plans must have hit a snag. (talk) 13:49, 15 August 2016 (UTC)

Bias sentence[edit]

"The function was called the "Smarandache function" in a 1980 publication by Florentin Smarandache that noted the existence of many other publications on the subject but cited none of them.[5]"
This is false again. You compromise Wikipedia by inserting biased, untrue ideas. Please do not delete my response. My paper was called A Function in the Number Theory (1980), see the paper as it was published, not Smarandache Function. Nowhere in the paper it was called Smarandache Function, but it was called "function \eta". Please ask NSA and CIA and wikipedians from Timisoara to check at the University of Timisoara library the paper printed journal An. Univ. Timisoara, Seria St. Matematice, Vol. XVIII, Fasc. 1, pp. 79-88, 1980; see Mathematical Reviews: 83c : 10008, to get convinced that I DID NOT CALLED IT SMARANDACHE FUNCTION.
Please stop continuously insulting me and inventing lies about me. (Florentin Smarandache) — Preceding unsigned comment added by FlSmarandache (talkcontribs) 16:29, 19 October 2016 (UTC)

The error was believing that the 2004 arXiv version of your paper was an accurate reproduction of the 1980 journal paper. The part where it calls it the Smarandache function, mentions past work, and doesn't cite any, is footnote 1 of the arXiv version. —David Eppstein (talk) 17:24, 19 October 2016 (UTC)

False statement again[edit]

“The function was called the "Smarandache function" in a 2004 publication by Florentin Smarandache that noted the existence of many other publications on the subject but cited none of them.” This is not true.
The function became popular as the Smarandache function after the publication of the books by C. Dumitrescu & V. Seleacu (1996) and Charles Ashbacher (1995, 1998). These publications were one decade before I included that note into my arXiv paper where I actually meant as citations these books, so they deserve to be cited first.
C. Dumitrescu, V. Seleacu, The Smarandache function, Vail, AZ : Erhus Univ Press, 1996; see the Library of Congress record on this book:
Charles Ashbacher, An Introduction to the Smarandache Function, Vail, 1995, 60 p. Charles Ashbacher, Pluckings from the tree of Smarandache: sequences and functions, Lupton, AZ : American Research Press, 1998; see the Library of Congress record on this book:
Please check the Library of Congress for the above hard copy books and document yourself (I gave you above two links). Please stop continuously incriminating me and spreading out unverified statements in Wikipedia! (Florentin Smarandache) — Preceding unsigned comment added by FlSmarandache (talkcontribs) 18:01, 26 October 2016 (UTC)

So when you say your footnote was meant to serve as a reference to these books, that means that by 2004 (24 years after the original publication of your paper) you were still unaware of the earlier work by Lucas, Neuberg, and Kempner? This despite the existence of the paper "The Smarandache function introduced more than 80 years ago!" by József Sándor in Octogon Mathematical Magazine, 2001? —David Eppstein (talk) 18:37, 26 October 2016 (UTC)