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Sum-Product Number
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Details
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. A sum-product number is an integer that in a given base is equal to the sum of its digits times the product of its digits. Or, to put it algebraically, given an integer n that is l digits long in base b (with dx representing the xth digit), if n = (sum{i = 1}^l di)(prod{j = 1}^l dj) then n is a sum-product number in base b. In base 10, the only sum-product numbers are 0, 1, 135, 144 (sequence A038369 in OEIS). Thus, for example, 144 is a sum-product number because 1 + 4 + 4 = 9, and 1 × 4 × 4 = 16, and 9 × 16 = 144. Obviously, 1 is a sum-product number in any base, because of the multiplicative identity. 0 is also a sum-product number in any base, but no other integer with significant zeroes in the given base can be a sum-product number. 0 and 1 are also unique in being the only single-digit sum-product numbers in any given base; for any other single-digit number, the sum of the digits times the product of the digits works out to the number itself squared.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131234736
- Editor Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow
- Größe H220mm x B220mm
- EAN 9786131234736
- Format Fachbuch
- Titel Sum-Product Number
- Herausgeber Betascript Publishing
- Anzahl Seiten 108
- Genre Mathematik
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