Hmm... if you are using EF6, this is actually a lot easier than you might think. Just open your model, right click on the column you want to set a default for, choose properties, and you will see a "DefaultValue" field. Just fill that out and save. It will set up the code for you.
The problem with some of the other solutions, it that while they may work initially, as soon as you rebuild the model, it will throw out any custom code you inserted into the machine-generated file.
So under the hood the UI works by adding an extra property to the edmx file:
<EntityType Name="Thingy">
<Property Name="Iteration" Type="Int32" Nullable="false" **DefaultValue="1"** />
And by adding the necessary code to the constructor:
public Thingy()
{
this.Iteration = 1;