%I #27 Mar 01 2023 04:38:17

%S 0,0,1,0,2,0,2,2,4,0,4,0,2,6,7,0,4,0,4,10,6,0,6,6,4,6,10,0,6,0,4,8,6,

%T 6,21,0,2,6,18,0,6,0,4,18,10,0,8,10,10,12,12,0,6,16,22,14,6,0,10,0,2,

%U 12,21,12,20,0,4,10,22,0,10,0,2,12,20,14,24,0,8,24,8,0,10,28,6,6,18,0,10

%N Number of different nontrivial two-digit cancellations of the form (xy)/(zx) = y/z in base n.

%C Trivial cancellations are of the form xx/xx=x/x, e.g. 44/44 = 4/4.

%D Boas, R. P. "Anomalous Cancellation," Ch. 6 in Mathematical Plums (Ed. R. Honsberger). Washington, DC: Math. Assoc. Amer., pp. 113-129, 1979.

%H Ludovic Schwob, <a href="/A094907/b094907.txt">Table of n, a(n) for n = 2..1000</a>

%H R. P. Boas, <a href="http://www.jstor.org/stable/3026913">Anomalous Cancellation</a>, The Two Year College Mathematics Journal, Vol. 3, No. 2 (Autumn 1972), 21-24.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AnomalousCancellation.html">Anomalous Cancellation</a>.

%F From _Ludovic Schwob_, Nov 10 2020: (Start)

%F a(n)=0 if and only if n is prime.

%F a(n) is odd if and only if n is an even square. (End)

%e a(10) = 4 because we have the four nontrivial base-10 cancellations 64/16 = 4/1, 65/26 = 5/2, 95/19 = 5/1, 98/49 = 8/4.

%t a[n_]:= Length[(DeleteCases[ #1, {u_, u_, u_}] & )[ Position[Table[(n*x + y)/(n*z + x) == y/z, {x, 1, n - 1}, {y, 1, x - 1}, {z, 1, y - 1}], True]]]

%K nonn,base

%O 2,5

%A Rick Mabry (rmabry(AT)pilot.lsus.edu), Jun 16 2004