A094907 - OEIS

A094907

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

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

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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

Ludovic Schwob, Table of n, a(n) for n = 2..1000

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

Adjacent sequences: A094904 A094905 A094906 * A094908 A094909 A094910

KEYWORD

nonn,base

AUTHOR

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

STATUS

approved