Where is the infinite (99) lives staircase in the original Super Mario Bros?

It appears to be at the end of stage 3-1. (source)

I've unfortunately never been able to perform this trick. The potential of 99 lives does you no good if you die every time you go for it.

It is the level 3-1.

There is another one in Stage 7-1 with a Buzzy Beetle at the end staircase.