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Base-dependent integer sequences: Palindromic number, Transposable integer, Happy number, Repunit, Narcissistic number, Harshad number: Palindromic ... Polydivisible number, Pandigital number - Softcover
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 26. Chapters: Palindromic number, Transposable integer, Happy number, Repunit, Narcissistic number, Harshad number, Self number, Automorphic number, Look-and-say sequence, Home prime, Friedman number, Polydivisible number, Pandigital number, Self-descriptive number, Vampire number, Kaprekar number, Parasitic number, Smith number, Palindromic prime, Circular prime, Sum-product number, Factorion, Truncatable prime, Dihedral prime, Permutable prime, Smarandache-Wellin number, Maris-McGwire-Sosa pair, Weakly prime number, Primeval number, Keith number, Minimal prime, Strobogrammatic prime, Strobogrammatic number, Frugal number, Emirp, Extravagant number, Repdigit, Dudeney number, Undulating number, Trimorphic number, Equidigital number. Excerpt: The digits of some specific integers permute or shift cyclically when they are multiplied by a number n. Examples are: These specific integers, known as transposable integers, can be but are not always cyclic numbers. The characterization of such numbers can be done using repeating decimals (and thus the related fractions), or directly. For any integer coprime to 10, its reciprocal is a repeating decimal without any non-recurring digits. E.g. = 0.006993... While the expression of a single series with vinculum on top is adequate, the intention of the above expression is to show that the six cyclic permutations of 006993 can be obtained from this repeating decimal if we select six consecutive digits from the repeating decimal starting from different digits. This illustrates that cyclic permutations are somehow related to repeating decimals and the corresponding fractions. The greatest common divisor (gcd) between any cyclic permutation of an m-digit integer and 10 − 1 is constant. Expressed as a formula, where N is an m-digit integer; and Nc is any cyclic permutation of N. For example, gcd(0915...
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- PublisherBooks LLC, Wiki Series
- Publication date2011
- ISBN 10 1156113539
- ISBN 13 9781156113530
- BindingTapa blanda
- LanguageEnglish
- Number of pages28
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Base-dependent integer sequences
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Reference Series Books LLC Okt 2011, 2011
ISBN 10: 1156113539
ISBN 13: 9781156113530
New
Taschenbuch
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Source: Wikipedia. Pages: 26. Chapters: Palindromic number, Transposable integer, Happy number, Repunit, Narcissistic number, Harshad number, Self number, Automorphic number, Look-and-say sequence, Home prime, Friedman number, Polydivisible number, Pandigital number, Self-descriptive number, Vampire number, Kaprekar number, Parasitic number, Smith number, Palindromic prime, Circular prime, Sum-product number, Factorion, Truncatable prime, Dihedral prime, Permutable prime, Smarandache Wellin number, Maris-McGwire-Sosa pair, Weakly prime number, Primeval number, Keith number, Minimal prime, Strobogrammatic prime, Strobogrammatic number, Frugal number, Emirp, Extravagant number, Repdigit, Dudeney number, Undulating number, Trimorphic number, Equidigital number. Excerpt: The digits of some specific integers permute or shift cyclically when they are multiplied by a number n. Examples are: These specific integers, known as transposable integers, can be but are not always cyclic numbers. The characterization of such numbers can be done using repeating decimals (and thus the related fractions), or directly. For any integer coprime to 10, its reciprocal is a repeating decimal without any non-recurring digits. E.g. = 0.006993. While the expression of a single series with vinculum on top is adequate, the intention of the above expression is to show that the six cyclic permutations of 006993 can be obtained from this repeating decimal if we select six consecutive digits from the repeating decimal starting from different digits. This illustrates that cyclic permutations are somehow related to repeating decimals and the corresponding fractions. The greatest common divisor (gcd) between any cyclic permutation of an m-digit integer and 10 - 1 is constant. Expressed as a formula, where N is an m-digit integer; and Nc is any cyclic permutation of N. For example, gcd(091575, 999999) = gcd(3×5×11×37, 3×7×11×13×37) = 3663 = gcd(915750, 999999) = gcd(157509, 999999) = gcd(575091, 999999) = gcd(750915, 999999) = gcd(509157, 999999)If N is an m-digit integer, the number Nc, obtained by shifting N to the left cyclically, can be obtained from: where d is the first digit of N and m is the number of digits. This explains the above common gcd and the phenomenon is true in any base if 10 is replaced by b, the base. The cyclic permutations are thus related to repeating decimals, the corresponding fractions, and divisors of 10-1. For examples the related fractions to the above cyclic permutations are thus: Reduced to their lowest terms using the common gcd, they are: That is, these fractions when expressed in lowest terms, have the same denominator. This is true for cyclic permutations of any integer. An integral multiplier refers to the multiplier n being a 26 pp. Englisch. Seller Inventory # 9781156113530
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Base-dependent integer sequences : Palindromic number, Transposable integer, Happy number, Repunit, Narcissistic number, Harshad number, Self number, Automorphic number, Look-and-say sequence, Home prime, Friedman number, Polydivisible number, Pandigital number
Published by
Books LLC, Reference Series, 2011
ISBN 10: 1156113539
ISBN 13: 9781156113530
New
Taschenbuch
Seller: AHA-BUCH GmbH, Einbeck, Germany
Seller rating 5 out of 5 stars
Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Source: Wikipedia. Pages: 26. Chapters: Palindromic number, Transposable integer, Happy number, Repunit, Narcissistic number, Harshad number, Self number, Automorphic number, Look-and-say sequence, Home prime, Friedman number, Polydivisible number, Pandigital number, Self-descriptive number, Vampire number, Kaprekar number, Parasitic number, Smith number, Palindromic prime, Circular prime, Sum-product number, Factorion, Truncatable prime, Dihedral prime, Permutable prime, Smarandache Wellin number, Maris-McGwire-Sosa pair, Weakly prime number, Primeval number, Keith number, Minimal prime, Strobogrammatic prime, Strobogrammatic number, Frugal number, Emirp, Extravagant number, Repdigit, Dudeney number, Undulating number, Trimorphic number, Equidigital number. Excerpt: The digits of some specific integers permute or shift cyclically when they are multiplied by a number n. Examples are: These specific integers, known as transposable integers, can be but are not always cyclic numbers. The characterization of such numbers can be done using repeating decimals (and thus the related fractions), or directly. For any integer coprime to 10, its reciprocal is a repeating decimal without any non-recurring digits. E.g. = 0.006993. While the expression of a single series with vinculum on top is adequate, the intention of the above expression is to show that the six cyclic permutations of 006993 can be obtained from this repeating decimal if we select six consecutive digits from the repeating decimal starting from different digits. This illustrates that cyclic permutations are somehow related to repeating decimals and the corresponding fractions. The greatest common divisor (gcd) between any cyclic permutation of an m-digit integer and 10 - 1 is constant. Expressed as a formula, where N is an m-digit integer; and Nc is any cyclic permutation of N. For example, gcd(091575, 999999) = gcd(3×5×11×37, 3×7×11×13×37) = 3663 = gcd(915750, 999999) = gcd(157509, 999999) = gcd(575091, 999999) = gcd(750915, 999999) = gcd(509157, 999999)If N is an m-digit integer, the number Nc, obtained by shifting N to the left cyclically, can be obtained from: where d is the first digit of N and m is the number of digits. This explains the above common gcd and the phenomenon is true in any base if 10 is replaced by b, the base. The cyclic permutations are thus related to repeating decimals, the corresponding fractions, and divisors of 10-1. For examples the related fractions to the above cyclic permutations are thus: Reduced to their lowest terms using the common gcd, they are: That is, these fractions when expressed in lowest terms, have the same denominator. This is true for cyclic permutations of any integer. An integral multiplier refers to the multiplier n being a. Seller Inventory # 9781156113530
Quantity: 1 available