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

1,1

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.

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

Table of n, a(n) for n=1..30.

Shalosh B. Ekhad, Automated Generation of Anomalous Cancellations, arXiv:1709.03379 [math.HO], 2017.

Eric W. Weisstein, Anomalous Cancellation.

Formula

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

Example

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.

Crossrefs

Cf. A159976 (denominators)

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

Sequence in context: A246451 A295327 A179202 * A350300 A110623 A163674

Adjacent sequences: A159972 A159973 A159974 * A159976 A159977 A159978

Keyword

base,fini,frac,full,nonn

Author

Jonathan Vos Post, Apr 28 2009

Status

approved