Hafsokos

Since there are many Shabossos in a row with Yotzeros (from Shabbos Shkolim until Shvi'i shel Pesach), it is considered an "insult" for the Shabbos to skip it and not say Yotzeros, therefore they were said at the Hafsokos too.
We see the similar logic with 2nd of Sivan - the first is Rosh Chodesh, the 3rd 4th and 5th are 3 days of Hagbolo and no Tachanun can be said, but actually there is no reason not to say Tachanun on the 2nd of Sivan. Anyhow - Tachanun is not said at that day, in order not to "insult" it, since it is between days without Tachanun, (therefore it is called in Loshon Sagi Nehor "Yom Hameyuchos", the special day).

Michael FRBSH