osmiframe
The standard iframe generated by OSM use 4 coordinates to set the view zone (in a bbox parameter).
This repo provide a thin wrapper that allows to use 3 parameters : the center coordinates (lat, lon) and the zoom factor (z).
Here is an example of use
<iframe src="https://kpym.github.io/osmiframe/?lat=48.8583&lon=2.2945&z=17"
width="400" height="210" frameborder="0"></iframe>
And you can see the result in example.html.
If you need IE support you can use https://kpym.github.io/osmiframe/ie/ as replacement. This version loads url-polyfill.