cp's OEIS Frontend

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

%I A159975 #16 Feb 16 2025 08:33:10
%S A159975 13,16,19,26,124,127,138,139,145,148,154,161,163,166,176,182,187,187,
%T A159975 187,199,218,266,273,275,286,316,327,364,412,436
%N A159975 Numerators (with multiplicity) of proper solutions up to 3-digit denominators of fractions with anomalous cancellation.
%C A159975 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.
%D A159975 Boas, R. P. "Anomalous Cancellation." Ch. 6 in Mathematical Plums (Ed. R. Honsberger). Washington, DC: Math. Assoc. Amer., pp. 113-129, 1979.
%D A159975 Moessner, A. Scripta Math. 19; 20.
%D A159975 Ogilvy, C. S. and Anderson, J. T. Excursions in Number Theory. New York: Dover, pp. 86-87, 1988.
%H A159975 Shalosh B. Ekhad, <a href="https://arxiv.org/abs/1709.03379">Automated Generation of Anomalous Cancellations</a>, arXiv:1709.03379 [math.HO], 2017.
%H A159975 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/AnomalousCancellation.html">Anomalous Cancellation</a>.
%F A159975 a(n)/A159976(n) is a proper fraction which undergoes Anomalous Cancellation.
%e A159975 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.
%Y A159975 Cf. A159976 (denominators)
%Y A159975 For other fractions like this see A291093/A291094, A290462/A290463.
%K A159975 base,fini,frac,full,nonn
%O A159975 1,1
%A A159975 _Jonathan Vos Post_, Apr 28 2009