A051070 is a self-referential OEIS sequence where a(n) equals the n-th term of sequence A_n, producing paradoxes and subway stop entries.
Key Takeaways
A051070 encodes a diagonal slice across all OEIS sequences: a(n) = A_n(n), returning -1 when A_n lacks enough terms.
a(53) and a(54) are -1 because A000053 and A000054 are NYC subway stop lists (1 Train, Lexington Ave) with too few entries.
a(58) has 58,669,977,298,272,603 digits; a(66) is unknown because A000066 (trivalent graph girth) is only computed to 12 vertices.
A102288, defined as 1 + A_n(n), cannot have a self-consistent value at index 102288, making it deliberately paradoxical; Neil Sloane explicitly defended the paradox over M. F. Hasler’s 2017 objection.
OEIS contains roughly a dozen real-world train line sequences; Sloane noted they appear on math quizzes and tests.
