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A159975 Numerators (with multiplicity) of proper solutions up to 3-digit denominators of fractions with anomalous cancellation. 8
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
base,fini,frac,full,nonn
AUTHOR
Jonathan Vos Post, Apr 28 2009
STATUS
approved

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Last modified June 15 22:50 EDT 2024. Contains 373412 sequences. (Running on oeis4.)