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So... unless I'm not getting the concept right, 189 is not a Harshad number, is it? Since 1 + 8 + 9 = 18, and 189 / 18 = 10.5 , which is not an integer. What am I missing? — Preceding unsigned comment added by 213.61.58.164 ( talk) 09:53, 13 February 2012 (UTC)
The article says:
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)
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)
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 1044363342786. 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)
Is it Harshad or Harshard? Both appear multiple times in the article.
Why is it called a Harshad number ? Is Harshad name of a person ? Jay 07:06, 10 Nov 2004 (UTC)
Anyone know why the factorials are all Harshad numbers? Anyone know why it's only in base 10? -- Doradus 19:52, Nov 11, 2004 (UTC)
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)
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)
Although the article correctly identifies this property of "numbers" as base specific, I think it should explicitly point out the this is a property of number representation and not of numbers themselves. Any number is a Harshad Number if you choose the right base. Pure properties of numbers, e.g. primeness, are base independent. —Preceding unsigned comment added by 86.153.60.15 ( talk) 17:48, 26 January 2009 (UTC)
This sentence at the end of the introduction seems to contradict the list of Harshad numbers" "All integers between zero and n are Harshad numbers." Has a qualifying phrase been removed about bases or something? - DavidWBrooks ( talk) 13:11, 5 March 2009 (UTC)
The article says: "Interpolating zeroes into N will not change the sequence of digital sums, so it is possible to convert any solution into a larger one by interpolating a suitable number of zeroes" According to this statement, since 112 is a Harshad number in base 10 (1+1+2=4, and 122 is divisible by 4), so would 1102 - but it clearly isn't, since no umber ending in 02 is divisible by 4. 77.125.4.148 ( talk) 06:36, 29 March 2011 (UTC)
One thing I have always found with many of mathematics articles is a lack of information on relevance and uses. Coming from a science and engineering background, I see math as a tool, with a means to obtain expected results. I understand there are lots of mathematical terms that have no real basis in the world (or none currently discovered). I think it would be very useful and meaningful to include a section on application of the theories in the wiki, even if the application is something as basic as: "Recreational Mathematical Artifact or exercise with no known engineering application."
I do not know enough about Harshad numbers, but could see potential in cryptography that may go beyond recreational purpose. fter reading through the article, though, the only function I gleamed was that of recreational mathematics. If someone knows an application, please take a moment to write something up. It would be great to know if the theory is purely for entertainment purposes, a process searching for some special meaning, or something with proven real world applications. — Preceding unsigned comment added by 216.55.51.54 ( talk) 22:21, 3 April 2012 (UTC)
This article is completely misleading on the true history of Niven numbers or later renamed as harshad numbers. Niven talked about them and coined the phrase in a talk in 1977, while Cooper kennedy actually began discovering the details and proving them out in the early 1980's ... Proof below by references, it is easy to prove this page and even harshad and Niven's pages mentions as wrong in how they portray the minimal part of the two who made the original base proofs that allowed harshads work to be properly peer reviewed and proven out in the field of mathematics.
This is a good overview of the actual history with proper credit...
1985 paper...
http://www.hindawi.com/journals/ijmms/1985/386824/abs/
Articles which others reference correctly...
[2] Kennedy, R.E., Goodman, T., and Best, C., 1980, Mathematical discovery and Niven numbers, MATYC Journal, 14:21-25.
[3] Kennedy, R.E. and Cooper, C.N., 1984, On the natural density of the Niven numbers, College Mathematics Journal, 15:309-312.
[4] Saadatmanesh, M., Kennedy, R.E., and Cooper, C.N., 1992, Super Niven numbers, Mathematics in College, pp. 21-30. — Preceding unsigned comment added by Ichriskennedy ( talk • contribs) 12:33, 21 July 2015 (UTC)
The number 101010101010101010101 has digit sum 11 and divisible by 11. — Preceding unsigned comment added by 101.14.227.116 ( talk) 14:45, 10 September 2015 (UTC)
The c is explained, but what is the o in this formula? Just curious. N(x)=(c+o(1))\frac{x}{\log x} Genesyz ( talk) 00:47, 7 January 2018 (UTC)
Even though "Harshad" is not a surname, this is practically always spelled with a capital H. Someone changed the article to lower-case h throughout. That should be reverted. Try a Google Books search for evidence. 2A00:23C5:FE18:2700:95A:4C62:344C:BE14 ( talk) 07:13, 7 February 2022 (UTC)
quoting part of the definition, " integer that is divisible by the sum of its digits when written in that base." . Isn't it the case that, if x/(sum_digits) is an integer in the given base, then converting both x and the sum to any other base will also be integral? Cellocgw ( talk) 15:31, 26 March 2024 (UTC)
This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
So... unless I'm not getting the concept right, 189 is not a Harshad number, is it? Since 1 + 8 + 9 = 18, and 189 / 18 = 10.5 , which is not an integer. What am I missing? — Preceding unsigned comment added by 213.61.58.164 ( talk) 09:53, 13 February 2012 (UTC)
The article says:
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)
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)
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 1044363342786. 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)
Is it Harshad or Harshard? Both appear multiple times in the article.
Why is it called a Harshad number ? Is Harshad name of a person ? Jay 07:06, 10 Nov 2004 (UTC)
Anyone know why the factorials are all Harshad numbers? Anyone know why it's only in base 10? -- Doradus 19:52, Nov 11, 2004 (UTC)
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)
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)
Although the article correctly identifies this property of "numbers" as base specific, I think it should explicitly point out the this is a property of number representation and not of numbers themselves. Any number is a Harshad Number if you choose the right base. Pure properties of numbers, e.g. primeness, are base independent. —Preceding unsigned comment added by 86.153.60.15 ( talk) 17:48, 26 January 2009 (UTC)
This sentence at the end of the introduction seems to contradict the list of Harshad numbers" "All integers between zero and n are Harshad numbers." Has a qualifying phrase been removed about bases or something? - DavidWBrooks ( talk) 13:11, 5 March 2009 (UTC)
The article says: "Interpolating zeroes into N will not change the sequence of digital sums, so it is possible to convert any solution into a larger one by interpolating a suitable number of zeroes" According to this statement, since 112 is a Harshad number in base 10 (1+1+2=4, and 122 is divisible by 4), so would 1102 - but it clearly isn't, since no umber ending in 02 is divisible by 4. 77.125.4.148 ( talk) 06:36, 29 March 2011 (UTC)
One thing I have always found with many of mathematics articles is a lack of information on relevance and uses. Coming from a science and engineering background, I see math as a tool, with a means to obtain expected results. I understand there are lots of mathematical terms that have no real basis in the world (or none currently discovered). I think it would be very useful and meaningful to include a section on application of the theories in the wiki, even if the application is something as basic as: "Recreational Mathematical Artifact or exercise with no known engineering application."
I do not know enough about Harshad numbers, but could see potential in cryptography that may go beyond recreational purpose. fter reading through the article, though, the only function I gleamed was that of recreational mathematics. If someone knows an application, please take a moment to write something up. It would be great to know if the theory is purely for entertainment purposes, a process searching for some special meaning, or something with proven real world applications. — Preceding unsigned comment added by 216.55.51.54 ( talk) 22:21, 3 April 2012 (UTC)
This article is completely misleading on the true history of Niven numbers or later renamed as harshad numbers. Niven talked about them and coined the phrase in a talk in 1977, while Cooper kennedy actually began discovering the details and proving them out in the early 1980's ... Proof below by references, it is easy to prove this page and even harshad and Niven's pages mentions as wrong in how they portray the minimal part of the two who made the original base proofs that allowed harshads work to be properly peer reviewed and proven out in the field of mathematics.
This is a good overview of the actual history with proper credit...
1985 paper...
http://www.hindawi.com/journals/ijmms/1985/386824/abs/
Articles which others reference correctly...
[2] Kennedy, R.E., Goodman, T., and Best, C., 1980, Mathematical discovery and Niven numbers, MATYC Journal, 14:21-25.
[3] Kennedy, R.E. and Cooper, C.N., 1984, On the natural density of the Niven numbers, College Mathematics Journal, 15:309-312.
[4] Saadatmanesh, M., Kennedy, R.E., and Cooper, C.N., 1992, Super Niven numbers, Mathematics in College, pp. 21-30. — Preceding unsigned comment added by Ichriskennedy ( talk • contribs) 12:33, 21 July 2015 (UTC)
The number 101010101010101010101 has digit sum 11 and divisible by 11. — Preceding unsigned comment added by 101.14.227.116 ( talk) 14:45, 10 September 2015 (UTC)
The c is explained, but what is the o in this formula? Just curious. N(x)=(c+o(1))\frac{x}{\log x} Genesyz ( talk) 00:47, 7 January 2018 (UTC)
Even though "Harshad" is not a surname, this is practically always spelled with a capital H. Someone changed the article to lower-case h throughout. That should be reverted. Try a Google Books search for evidence. 2A00:23C5:FE18:2700:95A:4C62:344C:BE14 ( talk) 07:13, 7 February 2022 (UTC)
quoting part of the definition, " integer that is divisible by the sum of its digits when written in that base." . Isn't it the case that, if x/(sum_digits) is an integer in the given base, then converting both x and the sum to any other base will also be integral? Cellocgw ( talk) 15:31, 26 March 2024 (UTC)