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A094907 Number of different nontrivial two-digit cancellations of the form (xy)/(zx) = y/z in base n. 2
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,5
COMMENTS
Trivial cancellations are of the form xx/xx=x/x, e.g. 44/44 = 4/4.
REFERENCES
Boas, R. P. "Anomalous Cancellation," Ch. 6 in Mathematical Plums (Ed. R. Honsberger). Washington, DC: Math. Assoc. Amer., pp. 113-129, 1979.
LINKS
R. P. Boas, Anomalous Cancellation, The Two Year College Mathematics Journal, Vol. 3, No. 2 (Autumn 1972), 21-24.
Eric Weisstein's World of Mathematics, Anomalous Cancellation.
FORMULA
From Ludovic Schwob, Nov 10 2020: (Start)
a(n)=0 if and only if n is prime.
a(n) is odd if and only if n is an even square. (End)
EXAMPLE
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.
MATHEMATICA
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]]]
CROSSREFS
Sequence in context: A300236 A238158 A029906 * A343401 A226570 A158380
KEYWORD
nonn,base
AUTHOR
Rick Mabry (rmabry(AT)pilot.lsus.edu), Jun 16 2004
STATUS
approved

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Last modified July 25 02:23 EDT 2024. Contains 374585 sequences. (Running on oeis4.)