0,1

These numbers represent the smallest nontrivial examples (210=5.6.7=14.15, 720 = 2.3.4.5.6=8.9.10, 5040 = 2.3.4.5.6.7=7.8.9.10, 175560 = 19.20.21.22=55.56.57, 1729780=8.9.10.11.12.13.14=63.64.65.66.

Some patterns are impossible, e.g. x(x+1)(x+2)(x+3)=y(y+1) has been proved impossible.

Solutions to the equations: x(x+1)...(x+m)=y(y+1)...(y+n)

Sequence in context: A046402 A121479 A118279 this_sequence A009127 A046302 A118281

Adjacent sequences: A064221 A064222 A064223 this_sequence A064225 A064226 A064227

nonn

Jon Perry (perry(AT)globalnet.co.uk), Sep 22 2001