A290462 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.

64, 95, 96, 97, 291, 98, 294, 490, 1221, 1342, 65, 665, 1463, 2261, 1584, 97, 194, 98, 196, 392, 490, 830, 195, 98, 196, 294, 490, 197, 591, 199, 597, 995, 1393, 1791, 2321, 1443, 2442, 3441, 1160, 1165, 2563, 3961, 1586

Offset: 1

Author

N. J. A. Sloane, Aug 07 2017

Keywords

• nonn
• base
• fini
• full
• frac

Comments

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.

The numerator may have 2 or 3 digits.

For the denominators see A290463.

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

Examples

			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.
		

References

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

Links

• Doron Zeilberger, Table of n, a(n) for n = 1..171
• Doron Zeilberger, The complete list of pairs [abc, def]

Crossrefs

Cf. A290463.

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