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XI.—On the Sums of the Digits of Numbers
Published online by Cambridge University Press: 17 January 2013
Extract
The general properties of numbers, considered without reference to the notation in which they are expressed, have been very fully investigated by several of the most distinguished mathematicians. Little attention, however, has been paid to the particular properties resulting from the principle of the modern notation, which is the expression of every number in a series, a + bn + cn2, &c. where a, b, c, are the digits, and n the local value or root of the notation. Having been led to examine some of these results, and to account for them, I am now desirous of laying them before the Society. I do not flatter myself that they possess any great practical importance; but as I have reason to believe that they are new, I trust the Society will not think them entirely unworthy of their attention.
- Type
- Research Article
- Information
- Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 16 , Issue 2 , 1846 , pp. 87 - 98
- Copyright
- Copyright © Royal Society of Edinburgh 1846
References
page 93 note * In these equations, d 1, d 2, &c, express the 1st, 2d, &c., differences between the sums of the odd and even digits; S1 S2, &c., express the 1st, 2d, &c., sums of all the digits.