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Topic: 142857 (number)

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	Cyclic number - Wikipedia, the free encyclopedia
		A cyclic number is an integer in which cyclic permutations of the digits are successive multiples of the number.
		If leading zeros are not permitted on numerals, then 142857 is the only cyclic number in decimal.
		The known pattern to this sequence comes from algebraic number theory, specifically, this sequence is the set of primes p such that 10 is a primitive root modulo p.
	en.wikipedia.org /wiki/Cyclic_number (575 words)

	142857 (number) - Wikipedia, the free encyclopedia
		If you multiply the number by 2, 3, 4, 5, or 6, the answer will be a cyclic permutation of itself.
		In base 10, 142,857 is a Harshad number and a Kaprekar number.
		It is the repeating part in the decimal expansion of the rational number 1/7 = 0.
	en.wikipedia.org /wiki/142857_(number) (231 words)

	New Scientist Back Page - Numbers game (Site not responding. Last check: 2007-09-29)
		Finally, the set of prime numbers is known to be infinite, it is still conjecture as to whether the set of cyclic numbers is also infinite.
		142857 are the first six digits of the decimal representation of 1/7, obtained by the familiar long-division method: 7 into 10 gives 1 remainder 3, then 7 into 30 gives 4 remainder 2, then 7 into 20 gives 2 remainder 6, and so on.
		The number 142857 is the smallest cyclic number.
	www.newscientist.com /backpage.ns?id=lw314 (1154 words)

	Notable Properties of Specific Numbers at MROB
		A prime number, and one of many misspellings of the word "elite" used by those who wished to hide their conversations from automatic detection on bulletin-board systems in the 1990's.
		This number has a property which exemplifies some of the many, obscure and somewhat arbitrary investigations into number theory that can be explored by anyone with the interest (and perhaps a personal computer).
		It was then noticed that this is only one less than the number 196884 that occurs in the elliptic modular function responsible for the Ramanujan constant and connected to the proof of Fermat's Last Theorem.
	home.earthlink.net /~mrob/pub/math/numbers-10.html (2824 words)

	7 (number) - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-09-29)
		This horizontal stroke is, however, important to distinguish the glyph for seven from the glyph for one in writings that use a long upstroke in the glyph for one.
		The Magical Number Seven, Plus or Minus Two is the title of a 1956 paper by the cognitive psychologist George A. Miller which hypothesises that the effective channel capacity of human senses is equivalent to between 5 and 9 equally-weighted error-less choices.
		Number of John Elway, Hall of Fame QB of the Denver Broncos.
	www.myproxy.ca /nph-index.cgi/111110A/687474703a2f2f656e2e77696b6970656469612e6f72672f77696b692f536576656e (2806 words)

	Cantor's Diagonal Proof
		The new number is certainly in the set of real numbers, and it's certainly not on the countably infinite list from which it was generated.
		Number systems like what you are talking about have actually been developed, Simplicio, (see p-adic numbers) but the crucial difference is that the infinite sequence of digits is in the direction of increasing, not decreasing, significance, so the resulting implied "sum" does not converge to a value that behaves consistently like a magnitude.
		Simplicio: Irrational numbers, such as the square root of 2, are suggested as, in the number of digits in their decimal expansion, not having this bound.
	www.mathpages.com /home/kmath371.htm (1582 words)

	Number Tricks [I] mathematics,Funny Number Tricks...,by Manpreet,Pre School maths,preschool maths,nursury maths for ...
		The number after the unit digit in the final answer will always be the number initially conceived.
		You will find that the number after the unit digit in the answer is the number initially thought of i.e.
		It will be very clear to you by now that if you multiply 142857 by 2, 3, 4, 5, 6 you will get same figures in the same order, starting in a different place each time as if they were written round the edge of a circle.
	www.4to40.com /activities/mathemagic/index.asp?article=activities_mathemagic_numbertricks1 (745 words)

	The Reciprocal of Seven and Pi, the Ancient Reckoning System
		Again, the computations become infinite, whereby all of the historically significant numbers may be accomodated within the system related to the reciprocal of seven and the different values for pi, depending upon the different number of segments/degrees that a circle may be assigned.
		In this manner, the reciprocal-seven-like number, 1.142857 may be employed as the equivalent to the unit (diameter) one (1.0), for any circle's circumference (260c, 360c, etc.).
		The number of times that the length of the diameter of a circle may divide into the distance of the circumference of the circle has been shown to be 3.141592654 times in current studies.
	www.earthmatrix.com /serie103/pi-aztec.htm (3611 words)

	What's special about this number? (1)
		The dot and nine symbols were the earliest known forerunners of the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
		The 3184th Fibonacci number is an apocalypse number (Apocalpyse numbers are numbers having exactly 666 digits).
		Any large number is divisible by 11 if the difference between the sum of its odd digits (units, hundreds, etc.) and the sum of its even digits (tens, thousands, etc.) is 0 or a number divisible by 11.
	www.archimedes-lab.org /numbers/Num1_69.html (4278 words)

	What's a number?
		Given the difficulty of establishing whether a given number is algebraic or not, this was one of Cantor's early surprising results.
		The rest of the complex numbers could also be defined by adding this new number i to the set of reals and postulating that usual arithmetic operations (addition, subtraction, multiplication) apply to the expanded set and all the laws known to hold for these operations hold for the new set as well.
		The rest of surreal numbers (included are the numbers we discussed so far and myriads of numbers some of which I have a difficulty imagining.) are formed starting with 0 and applying just two simple rules.
	www.cut-the-knot.org /do_you_know/numbers.shtml (3546 words)

	Rational numbers (Site not responding. Last check: 2007-09-29)
		Rational number by definition is a number that can be represented by the form of "p/q" where p and q are non-zero integers.
		For example, giving a number (18/42), we get the modulo 42%18=6, so a common factor must exist in (18, 6); Further division will get a modulo of 0, so the common factor of original (18/42) is 6; We can easily get the answer (3/7) by removing the common factor 6.
		For a number num as p/q, p is numerator and q is denominator.
	ericlin2.tripod.com /mis/ration.html (1798 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-09-29)
		The length of the repeating part is the smallest number of 9's such that the denominator divides 9999...999000...0000 evenly.
		The number of zeroes in the number in the first line of this paragraph is just the larger of the two exponents of 2 and 5.
		Notice the 2 digits to the right of the decimal before the repeating part begins, corresponding to the two zeroes at the end of the number 99999900, corresponding to the larger of the exponents of 2 and 5 in the factorization of 9450.
	mathforum.org /library/drmath/view/54339.html (1732 words)

	Symbolism in the Sothic Cycle Number
		Irrespective of the manner in which the 1649.457812 number may have been communicated within the chosen numbers of the days in the Sothic Calendar, as we explained in the previous essay, the number serves functionally in relation to other historically significant numbers and day-counts.
		The number, in its own way, is designed to convey the significance of the number seven; a very sacred number of the ancient reckoning systems around the world.
		Inspite of the 1649457812 representing an apparently symbolic number, it may still be of computational significance in both math and geometry as expressed in the ancient reckoning systems and in the artwork.
	www.earthmatrix.com /sothicyc/extrac20.htm (981 words)

	Number 142857
		The 142857 is a very special number. In the following cases when this number is multiplied by different numbers from 1 to 6, the resulting number has the same digits as in the number 142857, only the order gets changed.
		if first number is 1 then it will be followed by 42857, if the first number is 2 then it will be followed 85714.
		The formation of this number can be understood by taking the reciprocal of the number 7 with which 142857 is very much related.
	www.geocities.com /vijaymankar/142857right.htm (391 words)

	7 (number) - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-09-29)
		The number of objects in the solar system visible to the naked eye, the classical "planets" (Moon, Mars, Mercury, Jupiter, Venus, Saturn, Sun).
		The numbers seven, seventy, seventy thousand, etc. are also used in Islamic traditions to denote an infinite or high number.
		On most phones, the 7 key is associated with the letters P, R, and S (there are a few phones that also put Q on 7, such as Sony Ericson cell phones), but on the BlackBerry it is the key for C and V.
	dictionpedia.com /en/7_(number) (2396 words)

	This is my Math page !!! (Site not responding. Last check: 2007-09-29)
		It is presumed that the intercourse among traders served to carry the symbols from country to country, and therefore a conglomeration from the four different sources.
		We define any number `x' raised to the power zero as 1, so that each power of `x' is one factor larger than the last.
		That means, when the number is multiplied by any number between 1 and 200, the product can always read off from a circle made up of the figures of the multiplicand.
	members.tripod.com /~aniketd/maths.html (1333 words)

	numcom19 (Site not responding. Last check: 2007-09-29)
		These are called asymptotic conjectures because they refer to the case when the number of primes investigated is extremely large.
		Also output the number of full period primes as a percentage of the total and compare your result with that of the first conjecture above.
		Count also the number of odd and even period lengths and compare your results with those predicted by the second conjecture.
	www.eng.um.edu.mt /~andebo/numbers/numcom19.htm (368 words)

	BBC - h2g2 - Unique Patterns Among Numerics
		The number 3 as it is well known, has the unusual property that if any multiple of 3 taken, its digits would add up to another multiple of 3.
		The number of digits to take is always one less than the length of the multiplying numbers, see shown examples) becomes the interior of the product, with the result carried over.
		The pattern continues, the fifth number is again one off the anagram of the last number in the sequence, followed by triple twos (note the repeating digits occur on every 3rd sequence instance).
	www.bbc.co.uk /dna/ww2/A12219833 (1012 words)

	142857 - A Calculator For One Seventh Repeating Decimal
		I have an article posted at Articles For Educators about the number 142857 (Here's the article link: My Pet Number - 142857.) I thought it would be fun to create a simple calculator that shows some of the oddities of 142857.
		In case you're interested, 142857 is not the only number that does such interesting stunts and tricks.
		142857 is the repeating decimal portion of one seventh (1/7 =.142857142857...).
	www.patio-de-recreo.com /huh_142857.asp (177 words)

	Toad Industries - Numbers, Harmonics, Math (Site not responding. Last check: 2007-09-29)
		Another strange quality of 142857 is if you multiply it by any number.
		If you arrange these numbers so each is displaced one number at a time you get the number 451326.
		Seven is a very harmonic number and is found in nature and many other places.
	toad69n.freeshell.org /numbers.html (370 words)

	Number 7
		The Number 7 has for ages been regarded as the Number of mystery relating to the spiritual side of things.
		Now add this number whenever you find it by natural addition, it will give you the figure 27, and as you have seen by the rule of natural addition described previously, you keep adding till only one number remains, to arrive at what is known as the root of the number.
		It is not a division of time that man would naturally adopt, it runs across all natural division of time," but this author, not seeing or perhaps knowing the great hidden truth contained in the number 7, worried only over the point, that it was not a division of time which man would naturally adopt.
	afgen.com /seven.html (785 words)

	Special Numbers I
		Believe it or not, but it is the smallest number that is expressable as the sum of two 4th powers in two different ways.
		If you select any prime number, greater than 3, square it, then diminish that by 1, then 24 is always a divisor (factor) of the result.
		Probably you recognize this number; it's the 6-digit period of the rational number 1/7.
	www.trottermath.net /numtrivia/specnum.html (1287 words)

	Angus's Personal Site: Fun with Maths
		Pick a three-digit number where the first and last digits are not the same, eg/ 590.
		It is easy to see why this will not work for numbers where the first and last digits are the same as the initial subtraction will give you zero.
		He noticed that the number of miles between his home and his mother's house and back again is the same as the number of miles he covers each week in going to and from work.
	www.angmail.fsnet.co.uk /mathfun1.htm (575 words)

	Multiplying by 142857
		Multiplying by 142857 can be difficult, but with a little practice it becomes quite easy.
		So when multiplying n x 142857 you should first divide by 7, (n DIV 7) and if the remainder (n MOD 7) is not 0, then write this number down.
		These numbers are easy to remember because if you notice the number 142857 and look at the numbers in (a.) – (f.), you will notice that the numbers just wrap around.
	sky.prohosting.com /numsense/Multiply_Numbers/Mult_142857.htm (189 words)

	[No title]
		It is the only known number that never changes the rotation of its digits, except when that number is equally divided by the multiple of 7.
		The one becomes your first number in your answer followed by the 5th lowest number of the tricky number that turns out to be the number 7.
		So, starting with your 1 that we got by dividing is 171428 and because you started by adding 1 you subtract the 1 from the end that would be a 5 less 1 or the answer is 1,714284.
	www.moesmagic.com /human-calc.html (426 words)

	The Pi sequency revealed ? - Above Top Secret Conspiracy Community
		What I try to show is that when I withdraw 2atan(142857) (the cycle number) with 4atan(1), I don't obtain a random pattern, like if I'd tryed it with an random number (like 123456) but a pattern based on 14 (2*7).
		You wont get any pattern if you try it with a random number, even if you try with 142855 or 142858 (142856 got also some weird properties, but we wont try to study 'em now).
		142857 is known as the cycle number, and have many weird properties.
	www.abovetopsecret.com /forum/thread59612/pg3 (2544 words)

	142857 - Number Theory And Math Classroom Projects
		It's a most amazing number, and it does tricks much more interesting than rolling over, or playing dead.
		Hopefully you noticed that both numbers contain the same digits: 1,2,4,5,7, and 8.
		For those who have some computer programming skill and knowledge of number theory, finding numbers that behave like 142857 is a good project.
	www.articlesforeducators.com /dir/mathematics/number_fun/pet_number_142857.asp (519 words)

	30 May 1999 Puzzle - Brian's Casio Calculator Corner
		When you multiply your number by any of the counting numbers 1, 2, 3, 4, 5, or 6, the resulting product must yield a six-digit number that contains the same set of digits as the six-digit number you originally selected.
		A search of a fairly large space (all six digit numbers!) with some complex solution criteria (digit counting, multiplication, digit counting of products) is certainly nothing you want to do by hand.
		We need these to be six-digit numbers after multiplying by numbers up to six — so the first digit has to be 1.
	brianhetrick.com /casio/p053099.html (668 words)

	142857 - My Pet Number - Comments and Discussion
		142857 - Number theory, classroom projects, exploration, and activities surrounding an unusual number with mysterious properties.
		My Pet Number - 142857, published in Directory : Mathematics : Fun With Numbers.
		You said that you've found some larger numbers (ie, the one with so many digits it has every 4-digit combination in it) that do the same thing as your pet number 142857.
	www.articlesforeducators.com /dir/mathematics/number_fun/pet_number_142857_comments.asp (282 words)

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