newlist = {{{17, -1}, {18, -1}, {19, -1}, {20, -1}}, {{16, -1}}, \
{{15, -1}}, {{14, -1}}, {{13, -1}}, {{12, -1}}, {{11, -1}}, {{10, \
-1}}, {{9, -1}}, {{8, -1}}, {{7, -1}}, {{6, -1}}, {{5, -1}}, {{4, \
-1}}, {{1, -1}, {2, -1}, {3, -1}}}
newrange = {60, 59, 55, 49, 44, 40, 34, 27, 21, 15, 9, 5, 3, 2, 1}
ListPlot[newlist, PlotMarkers -> Map[ToString, newrange], 
 PlotStyle -> Reverse[ColorData[3, "ColorList"]], Axes -> None]