# A Sequence from a Sequence

This is a sequence that I made. I poured by blood and sweat into this! OK, no, it was more like orange juice and yogurt. It wasn't really all that hard, I guess. It might be tricky to figure out, though! You'll know for sure when you've got it. Here's a fair warning, though, you're going to have to do some digging to confirm the 33rd term (that's the really big one).

0, 2, 1, 0, 2, 3, 0, 6, 6, 4, 44, 1, 180, 42, 16, 1096, 7652, 13781, 8,
24000, 119779, 458561, 152116956851941670912, 1054535, -53, 26, 27, 59,
4806078, 2, 35792568, 3010349, 2387010102192469724605148123694256128, 2,
0, -53, 43, 0, -4097, 173,...


I've given you the first 40 terms so there shouldn't be more than one possible answer. To help rule that out, though, I'll add this:

This is a finite list. You get an error if you try to get more than 52 terms.

• Good job finding one OEIS did not have! May 1, 2015 at 14:12
• how do you define an error here? May 1, 2015 at 14:28
• An error means that the next term can not be found because it doesn't exist. May 1, 2015 at 14:42
• @EngineerToast something like domain restriction or invalidation of logic by the term? OK. May 1, 2015 at 14:45
• "2387010102192469724605148123694256128"; 128, 256 hmm.. maybe... May 1, 2015 at 14:58

The next element is

$37338$

Open http://oeis.org/ , the world biggest database of known integer sequences.
You see that any sequence has an identifier number, for example the list of natural numbers is known as A000027.

How is Toast's list generated:

Starting from A000001, we take the $i_{th}$ number of the A00000$i_{th}$ sequence to build our one.

As you can see, A000001 starts with 0, so we consider 0 to build our sequence. Then, we take the second number of A000002, which is 2. Then, we consider the third number of A000003, which is 1. And so on...

The next term in the sequence is 37338, the 41th term of A000041.
Toast's list has only 52 terms because A000053 has only 29 numbers!

• How in the world did you arrive at this conclusion? May 1, 2015 at 18:23
• Do you really want to know? I admit it, I googled the big number! Ahah so smart! May 1, 2015 at 18:25
• Ahh! I didn't realize that it was already a sequence in OEIS! A091967 May 1, 2015 at 18:48
• Except for some reason the first term is 1 instead of 0.
– user88
May 2, 2015 at 13:16
• @JoeZ. That's because the entry A000000 doesn't exist. Jun 30, 2015 at 3:40