Continued sequences

[franktaw at netscape.net]

In the spirit of the recent list of sequences containing conjectured 
values, I have compiled a (no doubt partial) list of sequences having 
more values in various entries, but not included in the sequence itself 
because of uncertainty.  These might be appropriate for new index 
entries; some of them are also interesting research questions.

The main list is where some a(n) is not known, but a(m) for some m>n is 
known.  This list includes:

A001438, A002853, A005136, A006066, A016729, A027623, A037289, A048893, 
A051070, A063984, A064156, A068314, A068489, A070911, A072127, A072128, 
A072288, A074025, A077659, A078457, A078714, A078814, A080371, A080372, 
A080802, A088622, A091295, A091967, A094670, A098472, A098876, A100804, 
A103833, A105674, A105676, A105677, A109886, A110409, A112822, A113571, 
A114457, A118710, A119479, A119734, A121154.

This does not include sequences with a full set of values, plus 
additional ones; likewise excluding ones where the next term is too big 
to fit, but subsequent ones are smaller.

Second, sequences defined as sets where larger elements are known,  but 
it is not known if there are intermediate values:

A002982, A005849, A055233, A064593, A066289.

Third, sequences where constraints are shown for additional terms, but 
no definite values:

A060020, A060021, A105678, A107431.

Finally, sequences which show a conjectured continuation, again with no 
values known for certain:

A004137, A048873, A056287, A059813, A059817, A059818, A065106, A065107, 
A081082, A084619, A090659, A099260, A117342.

This does not include sequences which are conjectured to have no 
further terms.

Franklin T. Adams-Watters

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