When we were all young (old enough to understand numbers and whatever), my grandfather would recite the numbers above, then explain that those were the first (say) Wednesdays of the year. I remember that I pointed out to him that leap years screwed up the pattern, and he told me to shut up.
I always thought it was weird that he started with 3, but after my leap year experience, I didn't want to say anything. I had to admit, it was a pretty good thing to know, and I've used it to figure dates (although I can generally do that starting with today by adding or subtracting seven from today's date), but didn't know the significance of the numbers. Until today.
One of the devotions celebrated by the Catholic Church is the First Friday Devotion to the Sacred Heart of Jesus. Basically, for those of you who don't follow the link (you won't burst into flames, I promise), the devotion says that those who go to Mass and Communion on nine consecutive First Fridays are guaranteed a happy death, among other things. My grandfather would have known about this, probably learning it at school when he was in first grade, during the 1912-13 school year. Being a devout Catholic, he would have looked at the calendar for 1913 and discovered that the first Fridays were Jan 3, Feb 7, Mar 7, Apr 4, May 2, Jun 6, Jul 4, Aug 1, Sep 5, Oct 3, Nov 7, and Dec 5.
And since that pattern repeats in non-leap years, you can apply it to the first whatever of the year. Last year, it was Wednesday. Next year, it'll be Friday again. Since 2008 is a leap year, the pattern is for first Thursdays, and the pattern changes to 376315374264.
My grandfather was a bit of a man of mystery (his daughters always complained that he was as inscrutable as the Sphynx), but if you didn't think too hard about it, you realize he was a really beautiful guy.