

A159975


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


7



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
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OFFSET

1,1


COMMENTS

The set of all proper solutions up to 3digit 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. 113129, 1979.
Moessner, A. Scripta Math. 19; 20.
Ogilvy, C. S. and Anderson, J. T. Excursions in Number Theory. New York: Dover, pp. 8687, 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 * A110623 A163674 A280062
Adjacent sequences: A159972 A159973 A159974 * A159976 A159977 A159978


KEYWORD

base,fini,frac,full,nonn


AUTHOR

Jonathan Vos Post, Apr 28 2009


STATUS

approved



