# Harry's acceptance letters' count sequence

After ignoring the first letter, Harry was sent another one. Then 3, 12, 24. So the sequence would be 1, 1, 3, 12, 24, ...

Obviously, there are many sequences starting with these numbers. Is there any algorithm behind this? Since many muggles get those letters, and surely not all parents are keen on letting their children go to Hogwarts, I think we shouldn't think of this as random Harry-specific numbers. (Muggleborns don't just get letters, thanks @Dragona13) Let's get to the bottom of this!

• Probably not, since the letters were sent by Hagrid (who doesn't usually do this, but was given a chance to because it was Harry) and he was having a bit of fun! – Möoz Jan 13 '15 at 1:52
• But do we know it was Hagrid? And if it was him, he was perhaps just following the standard procedure when it comes to the amount of letters... although, true, it does seem like a bad idea in general to attract so much muggle attention. – Luka Mikec Jan 13 '15 at 1:58
• Given how bad JKR is at math, I'd say it's actually more likely that they're completely random. – phantom42 Jan 13 '15 at 2:13
• only 2 results on OEIS: oeis.org/… – calccrypto Jan 13 '15 at 3:11
• Muggleborn witches and wizards do not get letters but get instead a visit from a Hogwarts professor who explains everything to the parents. – Dragona13 Jan 13 '15 at 3:27

## There are lots of sequences, but none are relevant

For any initial values, there will be some sequence, even one defined by a rule, that has these initial values. As a simple demonstration, if the first n terms of a sequence indexed by i are given, one can simply fit a nth degree polynomial f(i) that has those terms as its values at 1, 2, 3 etc.

However, whatever sequence or sequences this might be, it is certainly not a very obvious one. And given J.K. Rowling's admitted dislike of mathematics, it seems unlikely that she had an obscure sequence in mind when writing the number of letters.

In particular, there are some in-plot reasons for the number of letters, which seem more compelling as a justification than some abstruse sequence.

• On Saturday, things began to get out of hand. Twenty-four letters to Harry found their way into the house, rolled up and hidden inside each of the two dozen eggs that their very confused milkman had handed Aunt Petunia through the living room window.

Harry Potter and the Sorcerer's Stone

So two dozen letters arrived, not because J.K. Rowling was following a mathematical rule, but because that's how many letters fit in two boxes of eggs at one per compartment.

In addition, the number of letters does not even follow the sequence given, nor do we really know how many there were.

• "No less than twelve" letters arrived, not exactly twelve:

On Friday, no less than twelve letters arrived for Harry. As they couldn't go through the mail slot they had been pushed under the door, slotted through the sides, and a few even forced through the small window in the downstairs bathroom.

Harry Potter and the Sorcerer's Stone

So while there are certainly many sequences that fit the number of letters, we cannot determine them from the book, nor is it likely that they were intentional.

The numbers constitute the 54th through the 58th members of the sequence A172497. In this sequence the next two numbers would be 36 and 72.