Conference rusure::math

1862.0. "Network service: Integer sequence finder." by CADSYS::COOPER (Topher Cooper) Fri Mar 25 1994 09:47

Newsgroups: rec.puzzles,sci.math,sci.physics
From: [email protected] (Chris Cole)
Subject: Announcement of new service on Internet
Summary: NJA Sloane's Sequence Server Announcement
Keywords: sequences, series
Date: Thu, 24 Mar 1994 20:19:26 GMT

I am posting the following announcement on behalf of Neil Sloane.

Announcement:

      The On-Line Encyclopedia of Integer Sequences
                   N. J. A. Sloane
        AT&T Bell Labs, Murray Hill, New Jersey

           with the assistance of Simon Plouffe
            Universite' du Quebec a' Montreal

To look up a sequence in the Encyclopedia, send mail to

[email protected]

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!

Notation:
%I = identification line: Annnn = absolute catalogue number of sequence,
        Nnnnn = number (if any) in "Handbook of Integer Sequences" (1973)
%S, %T = beginning of sequence
%N = name, %R = references, %Y = cross-references, %A = authority,
%F = formula (if not included in %N line),
%O = offset = [a,b]: a is subscript of first entry, b gives the
position of the first entry >= 2.
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 protected], 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

Of course the Annnn number has to be assigned by me, so use A0000 if sending
a new sequence.
The %S and %T lines are restricted to a total of 144 characters (digits and
commas only, no blanks)
The %N line may contain mathematical formulae, which are presently set in
troff (though tex or latex are also acceptable).
%R If a new sequence is from a preprint, please send me a copy (hard or soft),
also all available publication details.
If from a journal or book, please give all details, including page numbers.
%A Use your email address as the authority.  E.g. %A A0000 [email protected]
%O Described above, but here is an example:
	%S A2885 1,1,0,1,0,0,1,2,0,4,7,0,12,8,0,80,84,0,820
	%N A2885 Cyclic Steiner triple systems of order $2n+1$.
	%R A2885 GU70 504.
	%O A2885 0,8
The "0" means that the first entry gives the number of cyclic Steiner
systems of order 2n+1 when n=0.  The 8 means that the 8-th term is
the first that is >= 1 (this determines the place of the sequence
in the lexicographic order in the table).

    I believe Stan had a sequence of the form:
    
    	X[n] = X[n-1] + n * X[n-2]
    
    The first few terms are 1 1 4 8 28 76 272
    
    I sent it to the server and it came back empty. Oh, well.
    
      John

    Attached is a response from the server; I'm impressed, but then again,
    I'm easy.

Report:

 
Result of looking up  :
 
Result of looking up 1 3 7 12 18 26 35 45 56 69 :

%I A5228
%S A5228 1,3,7,12,18,26,35,45,56,69,83,98,114,131,150,170,191,213,236,260,
%T A5228 285,312,340,369,399,430,462,495,529,565,602,640,679,719,760,802,845,889,935
%N A5228 Sequence and first differences contain all numbers.
%R A5228 GEB 73.
%O A5228 1,2
%A A5228 njas

References (if any):

[GEB] =  D. R. Hofstadter,   G\" o del, Escher, Bach: An Eternal Golden Braid , Vintage Books, NY, 1980.

From:	US2RMC::"[email protected]"  5-MAY-1994 23:51:27.14

There is now a second program to identify sequences. This one will
not just look up the sequence in the Encyclopedia, it will also
try a large number of tricks in order to attempt to explain the
sequence. Send a message to
	[email protected]
containing 1 line like
lookup 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37

Start at the beginning, give lots of terms.  Minus signs are OK.
The program will try VERY hard to find an explanation.
There are probably still many bugs, since the program is complicated,
- please let me know if you find any.
I have made extensive use of programs of Bruno Salvy and Simon Plouffe.

Only one request may be submitted at a time, and (since this
program does some serious computing), only one request per user
per hour.  If there is no lookup line you will get the help file.

Neil Sloane, [email protected]