[seqfan] REPORT ON A051070 (the n-th term of sequence A_n, or -1)

[Neil Sloane]

The definition of A051050 is: a(n) is the n-th term of sequence A_n,
respecting the offset, or -1 if A_n has fewer than n terms.

Note that a(n) = -1 can arise in two ways: either A_n has fewer than n
terms, or A_n has at least n terms, but its n-th term is -1.

Here is a summary of the terms with n <= 80.

a(n) = -1 occurs just twice, for n = 53 and 54, in both cases because the
relevant New York subway lines do not have enough stops.

a(1) though a(65) are known, although a(58) = = 192523...920807 has
58669977298272603 digits.

a(66) is the first unknown value.

Also unknown for n <= 80 are a(67), a(72), a(74), a(75), a(76), and a(77)
(counts of numbers <= 2^n represented by various quadratic forms; some of
these do not even have b-files), and a(80), which like a(66) is a
graph-theory question.


Best regards
Neil

Neil J. A. Sloane, Chairman, OEIS Foundation.
Also Visiting Scientist, Math. Dept., Rutgers University,
Email: njasloane at gmail.com