A159975 Numerators (with multiplicity) of proper solutions up to 3-digit denominators of fractions with anomalous cancellation.

13, 16, 19, 26, 124, 127, 138, 139, 145, 148, 154, 161, 163, 166, 176, 182, 187, 187, 187, 199, 218, 266, 273, 275, 286, 316, 327, 364, 412, 436

Offset: 1

Author

Jonathan Vos Post, Apr 28 2009

Keywords

• base
• fini
• frac
• full
• nonn

Comments

The set of all proper solutions up to 3-digit denominators is given by 13/325, 16/64, 19/95, 26/65, 124/217, 127/762, 138/184, 139/973, 145/435, 148/185, 154/253, 161/644, 163/326, 166/664, 176/275, 182/819, 187/286, 187/385, 187/748, 199/995, 218/981, 266/665, 273/728, 275/374, 286/385, 316/632, 327/872, 364/637, 412/721, and 436/763.

Examples

			The first four values are the only four such cases for numerator and denominators of two digits: a(1) = 13 because 13/325 if you strike/cancel a digit "3" in numerator and denominator yields the correct 1/25. a(2) = 16 because 16/64 if you cancel a digit "6" in numerator and denominator yields the correct 1/4. a(3) = 19 because 19/95 if you cancel a digit "9" in numerator and denominator yields the correct 1/5.
		

References

• Boas, R. P. "Anomalous Cancellation." Ch. 6 in Mathematical Plums (Ed. R. Honsberger). Washington, DC: Math. Assoc. Amer., pp. 113-129, 1979.
• Moessner, A. Scripta Math. 19; 20.
• Ogilvy, C. S. and Anderson, J. T. Excursions in Number Theory. New York: Dover, pp. 86-87, 1988.

Links

• Shalosh B. Ekhad, Automated Generation of Anomalous Cancellations, arXiv:1709.03379 [math.HO], 2017.
• Eric W. Weisstein, Anomalous Cancellation.

Crossrefs

Cf. A159976 (denominators)

For other fractions like this see A291093/A291094, A290462/A290463.

Formula

a(n)/A159976(n) is a proper fraction which undergoes Anomalous Cancellation.