Number of Smith

A number of Smith is a number whose nap of its figures, in a given base, is equal to the sum of the figures of its Décomposition in product of factors first. In the case of the numbers which are not Without square, the decomposition is written without exhibitor S, by writing the repeated factor as often as necessary. For example, 202 is a number of Smith, since 2 + 0 + 2 = 4, and its decomposition is 2 × 101, and 2 + 1 + 0 + 1 = 4.

The prime numbers are not examined, since it is shown in an immediate way that all safisfont in the condition given above.

In bases 10, the increasing continuation of the numbers of Smith starts as follows:

4, 22, 27, 58, 85, 94, 121, 166,202,265,274,319,346,355,378,382,391,438,454,483,517,526,535,562,576,588,627,634,636,645,648,654,663, 666, 690,706,728,729,762,778,825,852,861,895,913,915,922,958,985,1086…

W.L. McDaniel in 1987 showed that there exists an infinity of numbers of Smith. There exist 29.928 numbers of Smith lower than a million. It is allowed that 3% of any million integers consecutive are numbers of Smith.

There exists an infinity of numbers of Smith Palindrome S.

The consecutive numbers of Smith (for example, 728 and 729,2964 and 2965) are called brothers Smith . One is unaware of how much Smith brothers exist.

The numbers of Smith were named by Albert Wilansky of the Université of Lehigh in the honor of his/her brother-in-law Harold Smith, who indicated the property in his phone number (4937775).

External bonds

  • Article in connection with the numbers of Smith on MathWorld (in English)

References

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