Q: How can I find the next number in this series? Are "complete this series" problems well defined?
S: Since there are infinitely many formulas that will fit any finite series, many people object that such problems have no good answer. But isn't this a special case of the general observation that theory is underdetermined by experience (in other words, that there are a lot of world views that are consistent with all the facts that we know)? And if so, doesn't this objection really apply to all puzzles? Isn't it just more obvious in the case of series puzzles?
As a long-time observer of rec.puzzles nit-picking, I have never seen a puzzle answer that could not be challenged. The list of assumptions made in solving any puzzle is neverending. Luckily, most of us share all or nearly all of these assumptions, so that we can agree on an answer when we see it.
All of this has a lot to do with topics such as computational complexity, algorithmic compressibility, Church's thesis, intelligence, and life.
- available via email. It is
AT&T Bell Labs, Murray Hill, New Jersey
To look up a sequence in the Encyclopedia, send mail to
containing a line of the form
lookup 4 9 16 25 36
for each sequence (up to a limit of 5) that you would like looked up.
The reply will report all sequences found in the Encyclopedia (up to a limit of 7) that match: your sequence, your sequence with 1 subtracted from each term, your sequence with 1 added to each term.
If there are too many matches, of course you should try again giving more terms!
References to journals give volume, page, year.
New sequences, comments, corrections, extensions, etc., accompanied whenever possible by references, should be sent to: N. J. A. Sloane, ATT Bell Labs, Room 2C-376, 600 Mountain Ave, Murray Hill, NJ 07974, USA. email: email@example.com, fax: 908 582 3340, voice: 908 582 2005
Ideally, new sequences and other contributions should follow the standard format, which is illustrated by:
%I A1034 N2311 %S A1034 60,168,360,504,660,1092,2448,2520,3420,4080,5616,6048,6072,7800, %T A1034 7920,9828,12180,14880,20160,25308,25920,29120,32736,34440,39732,51888 %N A1034 Orders of non-cyclic simple groups. %R A1034 DI58 309. LE70 137. ATLAS. %O A1034 1,1 %A A1034 njas
- here is an example