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Consider decimal fractions r = abc/def with b != 0, d != 0 such that r = ac/df, sorted first by def and then by abc; sequence gives the numerators abc.
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%I #30 Aug 22 2017 00:45:07

%S 64,95,96,97,291,98,294,490,1221,1342,65,665,1463,2261,1584,97,194,98,

%T 196,392,490,830,195,98,196,294,490,197,591,199,597,995,1393,1791,

%U 2321,1443,2442,3441,1160,1165,2563,3961,1586

%N Consider decimal fractions r = abc/def with b != 0, d != 0 such that r = ac/df, sorted first by def and then by abc; sequence gives the numerators abc.

%C These are "fractions with anomalous cancellation" of a particular type. Here the fractions are of the form abc/def, where the denominator has exactly three digits, such that if the tens digits (b and e) are canceled from the numerator and denominator the value is unchanged.

%C The numerator may have 2 or 3 digits.

%C For the denominators see A290463.

%C The full list of 171 terms is given in the a-file.

%D Doron Zeilberger, Email to N. J. A. Sloane, Aug 07 2017.

%H Doron Zeilberger, <a href="/A290462/b290462.txt">Table of n, a(n) for n = 1..171</a>

%H Doron Zeilberger, <a href="/A290462/a290462.txt">The complete list of pairs [abc, def]</a>

%e The first four fractions on the list are 64/160 = 4/10 (after cancelling the 6's!), 95/190 = 5/10, 96/192 = 6/12, 97/194 = 7/14.

%Y Cf. A290463.

%Y For other fractions with anomalous cancellation see A291093/A291094, A159975/A159976.

%K nonn,base,fini,full,frac

%O 1,1

%A _N. J. A. Sloane_, Aug 07 2017