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S·P numbers in bases other than 10

Published online by Cambridge University Press:  01 August 2016

Ezra Bussmann
Ezra Bussmann*
Affiliation:
Beloit College, 700 College St., Beloit, Wisconsin, USA
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Extract

In a recent issue of the Gazette, S. Parameśwaran introduced S·P numbers. A positive integer n is an S·P number if it equals the sum s of its digits multiplied by the product p of its digits, i.e. n = sp. Subsequently, H. J. Godwin showed that in any number base the number of S·P numbers is finite, and A. F. Beardon and K. Robin McLean enumerated all S·P numbers in base 10 (namely, 1, 135, and 144). We generalise Beardon’s technique from base 10 to an arbitrary base to determine all S·P numbers in bases 2 through 12. Contrary to the claims of Godwin, we find 4-digit and 5-digit S·P numbers in base 11.

Type
Articles
Information
The Mathematical Gazette , Volume 85 , Issue 503 , July 2001 , pp. 245 - 248
Copyright
Copyright © The Mathematical Association 2001

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References

1. Parameśwaran, S. Numbers and their digits—a structural pattern, Math. Gaz. 81 (July 1997) p. 263.CrossRefGoogle Scholar
2. Belcher, Paul Godwin, H. J. Lobb, Andrew Lord, Nick McLean, K. Robin and Williams, Phillip On S-P numbers, Math. Gaz. 82 (March 1998) pp. 72–75.Google Scholar
3. Beardon, A. F. S-P numbers, Math. Gaz. 83 (March 1999) pp. 25–32.Google Scholar
4. McLean, K. Robin There are only three S-P numbers, Math. Gaz. 83 (March 1999) pp. 32–39.Google Scholar