Two definitions of DCG measure
I believe you are correct, that the paper and Wikipedia disagree. The paper's formula suggests you apply no discount at $r &lt;= b$, which means both of the first two elements are not discounted.

The Wikipedia formula discounts the second element onward.

There's an impassioned statement in Talk about why the Wikipedia formula is right: https://en.wikipedia.org/wiki/Talk:Discounted_cumulative_gain

But I can't see why; it offers no reference other than observing that "it seems plainly wrong to not discount from the second element." I'll comment there.