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Topic: Kaprekar number

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	Number World ....... - :::.Sh@uRya'z.::: One Site Million Options
		22 is the number of partitions of 8.
		101 is the number of partitions of 13.
		231 is the number of partitions of 16.
	shaurya.exocrew.com /forum/index.php?showtopic=2119 (9841 words)

	[No title]
		is the number of planar partitions of 10.
		is the number of planar partitions of 11.
		is the number of planar partitions of 12.
	home.comcast.net /~tdk500/Specialno.html (6437 words)

	Discuter:Dattatreya Ramachandra Kaprekar - Wikipédia
		Kaprekar Routine -- from MathWorld The Kaprekar routine is an algorithm discovered in 1949 by D. Kaprekar for 4-digit numbers, but which can be generalized to k-digit numbers.
		A 'Harshad number' has been defined as a number which can be divided exactly by the sum of its digits.
		Discovered in 1949 by the Indian mathematician D.R. Kaprekar a self number or Colombian number is an integer which, in a...
	fr.wikipedia.org /wiki/Discuter:Dattatreya_Ramachandra_Kaprekar (619 words)

	[No title] (Site not responding. Last check: 2007-09-17)
		Kaprekar Numbers: 9 is the smallest Kaprekar Number apart from 1: 92 = 81, and 8 + 1 = 9.
		The first few Kaprekar numbers are 1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728, 4950, 5050, 7272, 7777, When an n-digit Kaprekar Number is squared and the right hand n-digits are added to the left hand n or n-1 digits, the result is the original number.
		120 is the smallest number having 16 divisors.
	personal.vsnl.com /moloyde/believe.doc (2359 words)

	Kaprekar number - Encyclopedia Glossary Meaning Explanation Kaprekar number (Site not responding. Last check: 2007-09-17)
		Kaprekar number - Encyclopedia Glossary Meaning Explanation Kaprekar number.
		In mathematics, a Kaprekar number is a number that, in a given base, when squared, can be split into two numbers with the same number of digits as the original number which add up to the original number again.
		For example, the 3-digit number 703 is a Kaprekar number, because 703² = 494209, which can be split into 494 and 209, and 494 + 209 = 703.
	www.encyclopedia-glossary.com /en/Kaprekar-number.html (244 words)

	Kaprekar Series
		Kaprekar 3.0 Released There are two main change...
		The Kaprekar Series Generator allows you to determine the kaprekar series for any given number of digits (ranging from 2 to 2,147,483,647).
		For a given number iteration number (y-axis) against number at a given iteration (x-axis).
	kaprekar.blogspot.com (742 words)

	Notable Properties of Specific Numbers at MROB
		If you replace both numbers with their average, you get 32×32=1024, and 1024 is another number with important properties related to the fact that it is close to 1000.
		The numbers with this property are: 1, 8, (10), 45, 297, 2322, 2728, 4445, 4544, 4949, 5049, 5455, 5554, 7172, 27100, 44443, 55556, 60434, 77778, 143857,...
		The number that most Americans know best from its use as a speed limit also happens to be a Fibonacci number and the sum of the numbers 1 through 10 (which makes it the 10th triangular number).
	home.earthlink.net /~mrob/pub/math/numbers-5.html (2506 words)

	What's Special About This Number? (Site not responding. Last check: 2007-09-17)
		is the number of conjugacy classes in the automorphism group of the 8 dimensional hypercube.
		is the smallest of 6 consecutive numbers divisible by 6 consecutive primes.
		is the number of graceful permutations of length 12.
	www.stetson.edu /~efriedma/numbers.html (7257 words)

	► whose is d r kaprekar
		The answer to "whose is d r kaprekar" is coming soon.
		Do you have a good answer to the queston: "whose is d r kaprekar?" If so, please Submit an answer.
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	www.faq-site.com /faqs/157/whose-is-d-r-kaprekar.html (331 words)

	5000 (number) article - 5000 (number) natural number List numbers Integers << 1k 2k 3k 4k 6k - What-Means.com (Site not responding. Last check: 2007-09-17)
		Five thousand (5000) is the natural number following 4999 and preceding 5001.
		5777 - smallest counterexample to the conjecture that all odd numbers are of the form $p + 2a^2$
		5000 (number) article - 5000 (number) definition - what means 5000 (number)
	www.what-means.com /encyclopedia/5000 (123 words)

	The Kaprekar Numbers
		In particular, this establishes the correctness of an algorithm for generating the Kaprekar numbers proposed by Charosh in 1981.
		The Kaprekar numbers (sequence A006886 in [4]) were introduced by the eponymous D.
		The universal Kaprekar number 1 corresponds to the unitary divisor 1 of 10
	www.cs.uwaterloo.ca /journals/JIS/VOL3/iann2a.html (1251 words)

	Conrad Roche on the The Kaprekar Series (Site not responding. Last check: 2007-09-17)
		Kaprekar Series and Kaprekar Constants are numbers generated on applying the Kaprekar Routine on a number!
		The number of steps required to reach the number might be different, but sooner or later you'll land up with 6174.
		The Kaprekar Series Generator is a java application to help find all the Kaprekar Series for a specified number of digits.
	www.ansearch.com /cached/zfzdhazaznzs (684 words)

	Math words page 11
		Take a number (I'll use 45 as an example), square it (45^2 = 2025), and add the left half (20) to the right half(25) and if you get the number you started with, the number is a Kaprekar number.
		, thus the fifth Lucas number, 11, is the sum of the fourth and sixth fibonacci numbers (3+8).
		Sometimes pimorials are indicated by the number sign, #, which also goes by the names "pound sign", "octothorpe", "crosshatch", "tic-tac-toe", and in England and some international standards, "square".
	www.pballew.net /arithm11.html (4683 words)

	Kaprekar Sequences at MROB
		Thus, for example, since 45 is a 2-digit Kaprekar number we know that 55 is as well because 45+55 = 100.
		Although the reasons for Definition B are well-justified by the mathematics showing how to derive all the Kaprekar numbers, these reasons disappear when we discuss Kaprekar numbers for cubes and higher powers, where the aforementioned symmetry does not exist.
		Not all of the variations of each Kaprekar sequence are included in Sloane's catalog.
	home.earthlink.net /~mrob/pub/math/seq-kaprekar.html (482 words)

	Properties of 99 (Site not responding. Last check: 2007-09-17)
		A Kaprekar number is a number that, in a given base, the digits of its square can be split off into two numbers with as many digits as the original number, and these two new numbers add up to the original number.
		99 is a palindromic number, which is a symmetrical number written in some base A as a1 a2 a3......
		Although not really a cool numerical property, 99 is the atomic number of einsteinium.
	redkrane.net /clax/prop99.htm (167 words)

	► math- who is kaprekar
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		If your answer shows that you really know math- who is kaprekar, we will post it and link to your site to show our thanks for helping to build FAQ-Site into a valuable resource.
		Kaprekar Routine -- from MathWorld Kaprekar Routine -- from MathWorld The Kaprekar routine is an algorithm discovered in 1949 by D. Kaprekar for 4-digit numbers, but which can be generalized to k-digit numbers.
	www.faq-site.com /faqs/59/math--who-is-kaprekar.html (343 words)

	Kaprekar-6174
		Form a new number from this number by rearranging the digits in decreasing order, e.g.
		Reverse the number obtained in Step 2, then subtract the smaller number from the larger one.
		This is a famous number in the field of recreational mathematics; it's called Kaprekar's Constant.
	www.trottermath.net /recurops/kaprekar.html (451 words)

	Kaprekar Routine (Site not responding. Last check: 2007-09-17)
		The algorithm reaches 0 (a degenerate case), a constant, or a cycle, depending on the number of digits in
		Eldridge, K. and Sagong, S. ``The Determination of Kaprekar Convergence and Loop Convergence of All 3-Digit Numbers.'' Amer.
		Kaprekar, D. ``An Interesting Property of the Number 6174.'' Scripta Math.
	mathserver.sdu.edu.cn /mathency/math/k/k031.htm (191 words)

	numcom07 (Site not responding. Last check: 2007-09-17)
		This is a Kaprekar number because when we square it we get 4,941,729 and if we add the number formed by the last 4 digits of this result i.e.
		He found that the number 6174 is the result which one eventually obtains (with some exceptions) when one subtracts a 4-digit number whose digits are arranged in ascending order from the same number with the digits arranged in descending order.
		Thus the number 3289 took 5 steps to reach the 'magic' number 6174.
	www.eng.um.edu.mt /~andebo/numbers/numcom07.htm (304 words)

	sciforums.com - Kaprekar's number (Site not responding. Last check: 2007-09-17)
		Take any number (I think it was proved up to 11 digits), assuming that not all digits of the number are the same.
		Rewrite the number to be 10b + a
		3)all numbers that are less than 495, will produce a number that is greater than itself, and those that are greater will produce a number that is less than itself (ex.
	www.sciforums.com /printthread.php?t=26549 (333 words)

	math lessons - 100000 (number)
		One hundred thousand (100000) is the natural number following 99999 and preceding 100001.
		In astronomy, 100,000 metres, 100 kilometres, or 100 km (62 miles) is the altitude at which the Federation Aeronautique Internationale (FAI) defines spaceflight to begin.
		algebra arithmetic calculus equations geometry differential equations trigonometry number theory probability theory applied mathematics mathematical games mathematicians
	www.mathdaily.com /lessons/100000_(number) (118 words)

	MATHEWS: Kaprekar Numbers (Site not responding. Last check: 2007-09-17)
		Kaprekar numbers are named by D.R. Kaprekar who presented them 1980 in the Journal of Recreational Mathematics.
		M. Charosh 1981 noted Kaprekar's omission of this numbers and devised a method to construct large Kaprekar numbers.
		(Note that 1 is a Kaprekar number by convention and recall that a is a unitary divisor of m if ab=m and (a,b)=1).
	www.wschnei.de /digit-related-numbers/kaprekar-numbers.html (217 words)

	MathLinks Math Forum :: View topic - 6174=Kaprekar's constant
		between the numbers formed by writing the digits in descending order and ascending order.
		Iterate this process using the difference x_2 as the new 4-digit number.
		Kaprekar's constant, a fixed point of the iteration.
	www.mathlinks.ro /Forum/topic-29532.html (575 words)

	Kaprekar UML Model in SVG (Site not responding. Last check: 2007-09-17)
		The class diagrams for Kaprekar are in SVG format.
		Click on the version number under the "UML Docs (svg)" section.
		If you cannot view the diagrams or find that they are not displayed properly on your machine, do let me know (unless the problem is already listed below).
	kaprekar.sourceforge.net /uml_svg/umlsvgdocs.php (274 words)

	Articles - 5000 (number) (Site not responding. Last check: 2007-09-17)
		5050 - triangular number, Kaprekar number, sum of first 100 integers
		5188 - Ï(5189) = 2592, centered heptagonal number
		5777 - smallest counterexample to the conjecture that all odd numbers are of the form p + 2a
	www.lastring.com /articles/5000_(number) (154 words)

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