# 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! – the4seasons May 1 '15 at 14:12
• how do you define an error here? – RE60K May 1 '15 at 14:28
• An error means that the next term can not be found because it doesn't exist. – Engineer Toast May 1 '15 at 14:42
• @EngineerToast something like domain restriction or invalidation of logic by the term? OK. – RE60K May 1 '15 at 14:45
• "2387010102192469724605148123694256128"; 128, 256 hmm.. maybe... – RE60K May 1 '15 at 14:58

## 1 Answer

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? – Warlord 099 May 1 '15 at 18:23
• Do you really want to know? I admit it, I googled the big number! Ahah so smart! – leoll2 May 1 '15 at 18:25
• Ahh! I didn't realize that it was already a sequence in OEIS! A091967 – Engineer Toast May 1 '15 at 18:48
• Except for some reason the first term is 1 instead of 0. – Joe Z. May 2 '15 at 13:16
• @JoeZ. That's because the entry A000000 doesn't exist. – Engineer Toast Jun 30 '15 at 3:40