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Search: id:A094907
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| A094907 |
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Number of different nontrivial two-digit cancellations of the form (xy)/(zx) = y/z in base n. |
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+0
1
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| 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; listen)
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OFFSET
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2,5
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COMMENT
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Trivial cancellations are of the form xx/xx=x/x, e.g. 44/44 = 4/4.
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REFERENCES
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Boas, R. P. "Anomalous Cancellation," Ch. 6 in Mathematical Plums (Ed. R. Honsberger). Washington, DC: Math. Assoc. Amer., pp. 113-129, 1979.
Boas, R. P. "Anomalous Cancellation," The Two Year College Mathematics Journal, Vol. 3, No. 2 (Autumn 1972), 21-24.
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LINKS
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Eric Weisstein. Anomalous Cancellation
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EXAMPLE
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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.
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MATHEMATICA
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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]]]
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CROSSREFS
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Sequence in context: A117192 A078729 A029906 this_sequence A158380 A051734 A157898
Adjacent sequences: A094904 A094905 A094906 this_sequence A094908 A094909 A094910
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KEYWORD
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nonn
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AUTHOR
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Rick Mabry (rmabry(AT)pilot.lsus.edu), Jun 16 2004
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