Talk:Harshad number

From Wikipedia, the free encyclopedia

Mathematics Portal This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating:	Start Class	Low Priority	Field: Number theory
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Geometry guy 00:28, 23 June 2007 (UTC)

Contents 1 Error in statement of theorem 1.1 No error 2 Understatement of the century 3 Inconsistency 4 Origin ? 5 Factorials in base 10 6 Consecutive Harshad Numbers -- Generalization 7 Notability

[edit] Error in statement of theorem

The article says:

H.G. Grundman proved in 1994 that in base 10 there are no sequences with more than 20 consecutive Harshad numbers,

but there is a missing word here, since clearly there is a sequence with more than 20 consecutive Harshad numbers, namely the sequence of Harshad numbers, whose initial segment is cited at the top of the article. Perhaps this should say "arithmetic sequence"? -- Dominus 00:53, 9 May 2004 (UTC)

[edit] No error

I just misunderstood it. The article was apparently saying that there are no sequences of more than 20 consecutive numbers that are all Harshad numbers. I have reworded the article in a way I find clearer. -- Dominus 00:58, 9 May 2004 (UTC)

I find your way to be clearer, too. Thanks for clarifying it. PrimeFan 19:57, 9 May 2004 (UTC)

Ditto. I was trying to fix it, but realized I wasn't sure what it originally meant. Thanks. Grendelkhan 22:35, 2004 May 9 (UTC)

It is my pleasure to assist. -- Dominus 00:34, 10 May 2004 (UTC)

[edit] Understatement of the century

He [Grundmann] also found the smallest sequence of 20 consecutive integers that are all Harshad numbers; they exceed 10⁴⁴.

The above statement is correctish, but at the same time looks like a misinterpretation of the facts. Various sources claim that the 20 numbers in the sequence exceed 10^44363342786. I wasn't able to find more information, which is why I'm not editing the article right away.
—Herbee 22:43, 2004 May 12 (UTC)

MathWorld agrees, so i changed the article Illuvatar 17:16, 7 Sep 2004 (UTC)

[edit] Inconsistency

Is it Harshad or Harshard? Both appear multiple times in the article.

• I changed them to Harshad. It's the name of the article, it gets more google hits, and it shows up in mathworld. If it can also be spelled Harshard, we should mention it

[edit] Origin ?

Why is it called a Harshad number ? Is Harshad name of a person ? Jay 07:06, 10 Nov 2004 (UTC)

[edit] Factorials in base 10

Anyone know why the factorials are all Harshad numbers? Anyone know why it's only in base 10? --P3d0 19:52, Nov 11, 2004 (UTC)

Not all are: the article says 432! is the first which is not. But as an aside, factorials can be dived by a large number of numbers, while the higher the base, the smaller the sum of the digits, and so the more likely they are to divide into a factorial. --Audiovideo 17:35, 23 March 2007 (UTC)

[edit] Consecutive Harshad Numbers -- Generalization

Base 2 -> Infinitely many sequences of 4 consecutive numbers. Base 3 -> Infinitely many sequences of 6 consecutive numbers. ... Base 10 -> Infinitely many sequences of 20 consecutive numbers? [Article doesn't say it, but implies it, IMHO.] Does anyone know if this can be generalized? 70.178.215.64 11:08, 7 January 2006 (UTC)

[edit] Notability

I can see this has enough notability for an article, but does it have enough to be linked from each Harshad number. I don't see it as a notable fact about 300 or similar numbers --Audiovideo 17:38, 23 March 2007 (UTC)