[seqfan] Two "dumb" sequences and a question

[Ali Sada]

Hi everyone,

Please consider the two sequences below:

1) Sequence AX contains all OEIS sequences where the A number is a term in the sequence itself. For example, A000027 since 27 is a positive integer. 

2) Sequence AY contains all OEIS sequences where either: 
a) the A number is not a term in the sequence (e.g., A000040, since 40 is not a prime number), 
or 
b) we don’t know if the A number is a term in the sequence or not (e.g., A329697).

The question here is: Where should the number Y go? If we put it in sequence AY, then we know where it belongs and that contradicts the definition of AY.
Also, it couldn’t be part of AX because Y is not a term of AY.

I’m trying to have some basic understanding of set theory and I would really appreciate your feedback.

Best,

Ali