cp's OEIS Frontend

These are the numbered stops for the #6 train.

These are the numbered stops for the A train, as of February 2000.

The Dyckman Street station used to be called Dyckman Street--200th Street, though there was never a 200th Street. - Charles R Greathouse IV, Nov 26 2018

Formally abbreviated as The Blue Line (and known informally as 'The El'), the Market-Frankford Line extends East to West from slightly to the east of 2nd Street through the city line to the western suburbs at 63rd Street and then on to 69th Street Transportation Center, lined up almost entirely with the major dividing thoroughfare Market Street. It is actually a subway at the eastern end of this portion and through to beyond the 40th Street stop (a(1)-a(9) represent subway stops), passing under the Schuylkill River (along with trolley lines 10, 11, 13, 34 and 36) closer to 30th than to 15th Street. The only non-numbered stop on this end is suburban Milbourne between 63rd and 69th. The 'Frankford end' runs in a somewhat northeasterly direction and has all stops only with non-number names (and is entirely above ground). The semi-express A and B versions of the train both skip certain stops at peak travel times, and the only regular trains are unmarked or one of these two versions. The train is substituted for with bus service during overnight hours. - James G. Merickel, Mar 19 2014

This version ignores the offset of A_n and just counts from the beginning of the terms shown in the OEIS entry.

Thus a(8) = 6 because A_8 begins 1,1,2,2,3,4,5,6,... [even though A_8(8) is really 7].

The value a(n) = -1 could arise in two different ways, but it will be easy to decide which. - N. J. A. Sloane, Nov 27 2016

From M. F. Hasler, Sep 22 2013: (Start)

The value of a(91967) can be chosen at will.

Note that this sequence may change if the initial terms in A_n are altered, which does happen from time to time, usually because of the addition of an initial term.

After a(47), currently unknown, the sequence continues with a(48) = A48(47) = 1497207322929, a(49) = A49(48) = unknown, a(50) = A50(49) = unknown, a(51) = A51(50) = 1125899906842625, a(52)=97, a(53) = -1 (since A000053 has only 29 terms). (End)

a(58) = A000058(57) = 138752...985443 (29334988649136302 digits) is too large to include in the b-file. - Pontus von Brömssen, May 21 2022

a(n) = A091967(n) + 1, except when A_n has fewer than n terms, in which case a(n) = -1. Of course this means that a value a(n) = -1 could arise in two different ways, but it will be easy to decide which. - N. J. A. Sloane, Nov 27 2016

What is a(102288)?!

See A091967 and A051070 for much more about this type of sequence. See A107357 for the variant which respects the offset of A_n (and therefore isn't affected when a sequence is completed by missing initial values).

The definition of this sequence is used in the traditional 'diagonal' proof that there are uncountably many integer sequences. - Simon Nickerson (simonn(AT)maths.bham.ac.uk), Jun 28 2005

The term a(102288) has no possible value according to the present definition, so the definition of this term should be changed, including the possibility that the sequence is defined to be finite, with fewer than 102288 terms. (In that case, the (former, impossible) definition which would say that a(102288) = -1 because A102288 has fewer than 102288 terms, does not apply.) - The term a(47) is currently unknown, since A000047 is known only up to n = 35. - M. F. Hasler, Jan 20 2017

I disagree with the previous comment! I prefer the present, deliberately paradoxical, definition. - N. J. A. Sloane, Jan 20 2017

At present there is no stop at 96th St. There are two successive stops on 149th St: E 149th St and Grand Concourse, then E 149 St and 3rd Ave.

Alternative version of A000053, which is the main entry for this train.