jquery nth child that is currently visible

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:nth-child scans the children of the parent no matter what their styling is. The counting in :nth-child is relative to the parent element, not the previous selector. This is explained in the jQuery docs for :nth-child:

With :nth-child(n), all children are counted, regardless of what they are, and the specified element is selected only if it matches the selector attached to the pseudo-class.

Using a more simple method with each does exactly what you want:

$('#test li:visible').each(function (i) {
    if (i % 4 == 0) $(this).addClass('fourth-item');
});

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