Topic
Smith number
About: Smith number is a research topic. Over the lifetime, 2 publications have been published within this topic receiving 5 citations.
Papers
TL;DR: In this paper, the Smith number is defined as a composite number such as 4 = 2 x 2, 22 = 2 × 11, or 27 = 3 X 3 × 3, the sum of whose digits is the same as the sum number of digits in its representation as a product of primes.
Abstract: Wilansky [1] defined a Smith number to be a composite number such as 4 = 2 x 2, 22 = 2 x 11, or 27 = 3 X 3 X 3, the sum of whose digits is the same as the sum of the digits in its representation as a product of primes. Professor Wilansky's brother-in-law, H. Smith, had a telephone number, 4937775 = 3 X 5 x 5 x 65837, which is a Smith number, whence the name. Oltikar and Wayland [2] found larger Smith numbers, including one with 362 digits. In this note, I find much larger ones, including one with 7,158 digits. Generally, integers of this size are notoriously difficult to factor, but you will see that if you have large primes of certain forms, it is easy to find large Smith numbers from them. We can get an idea of the sparseness of Smith numbers from Wilansky's count of them. He found that there are 47 among the first 1,000 nonnegative integers, and between 28 and 42 in each of the next nine 1,000-integer intervals, the average there being 35.
6 citations
Journal Article•
TL;DR: In this paper, the authors demonstrate how to construct integers for which $m$ is a Smith number for any prime $P$ with a fixed, small digital sum, which relies on small digital sums in order that every multiplication process is free from carries.
Abstract: Using prime numbers whose digits are zeros and ones, we demonstrate how to construct integers $m$ for which $mP$ is a Smith number for any prime $P$ with a fixed, small digital sum. Conversely, using numbers with small digital sums, we can obtain Smith multiples of a given prime whose digits are zeros and ones. Our approach relies on small digital sums in order that every multiplication process is free from carries.
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2015 | 1 |
| 1986 | 1 |