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

1,1

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.

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]

Example

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.

Crossrefs

Cf. A290463.

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

Sequence in context: A303530 A119894 A138667 * A355790 A240527 A262743

Adjacent sequences: A290459 A290460 A290461 * A290463 A290464 A290465

Keyword

nonn,base,fini,full,frac

Author

N. J. A. Sloane, Aug 07 2017

Status

approved