Reply from On-Line Encyclopedia of Integer Sequences (fwd)

[Meeussen Wouter (bkarnd)]

In[1]:=Table[Length[Last[ContinuedFraction[Sqrt[3] n]]],{n,128}]
Out[1]=
{2, 2, 2, 2, 4, 8, 2, 4, 10, 4, 2, 8, 6, 2, 2, 8, 6, 20, 4, 8, 14, 8, 8, 12,
16, 2, 30, 2, 16, 4, 18, 16, 10, 20, 16, 20, 18, 8, 6, 12, 2, 12, 8, 8, 6,
20, 20, 20, 30, 36, 6, 2, 8, 68, 14, 2, 16, 32, 22, 4, 38, 18, 40, 36, 6,
28,
10, 20, 40, 8, 4, 40, 18, 22, 16, 12, 28, 2, 46, 20, 98, 8, 46, 8, 6, 16,
16,
24, 50, 16, 16, 28, 50, 48, 12, 48, 2, 30, 50, 28, 16, 12, 46, 8, 12, 16,
50,
52, 66, 36, 14, 4, 62, 28, 32, 28, 16, 64, 36, 8, 74, 30, 10, 14, 84, 36,
62,
72}

In[2]:=Table[Length[Last[ContinuedFraction[Sqrt[3^(2n+1)] ]]],{n,10}]
Out[2]=
{2, 10, 30, 98, 270, 818, 2382, 7282, 21818, 65650}

I don't grok RKG's "-- it's the ranks of terms in the
last seq that I sent which have value 2" in his last mail


Wouter.





-----Original Message-----
From: Richard Guy [mailto:rkg at cpsc.ucalgary.ca]
Sent: donderdag 25 oktober 2001 18:16
To: ogerard at ext.jussieu.fr; seqfan at ext.jussieu.fr; Neil J. A. Sloane
Subject: Reply from On-Line Encyclopedia of Integer Sequences (fwd)


Here's a raft of new sequences, if anyone thinks
they are worthwhile and has the patience to
compute them. The one below is the period lengths
of the continued fraction for sqrt(3n^2) for
n = 1, 2, 3, ...

Here are a few more terms:

2 2 2 2 4 8 2 4 10 4 2 8 6 2 2 8 6 20 4 8 14 8 8 12 16 2 28

Similar sequences may or may not be of interest
with 3 replaced by other squarefree numbers.

Also some subsequences may be quite striking, e.g.
for sqrt(3^(2k+1)) :  2 2 10 28 ... much bigger   R.



---------- Forwarded message ----------
Date: Thu, 25 Oct 2001 12:42:24 -0400 (EDT)
From: sequences-reply at research.att.com
To: rkg at cpsc.ucalgary.ca
Subject: Reply from On-Line Encyclopedia of Integer Sequences

Matches (up to a limit of 50) found for  2 2 2 2 4 8 2 4 10 4 2 8 6 2 2 8 6
20 4 8  :


Even though there are a large number of sequences in the table, at least
one of yours is not there! Please send it to me using
the submission form on the sequence web page
http://www.research.att.com/~njas/sequences/Submit.html
and I will (probably) add it!  Include a brief description. Thanks!


===============================
This email is confidential and intended solely for the use of the individual to whom it is addressed. 
If you are not the intended recipient, be advised that you have received this email in error and that any use, dissemination, forwarding, printing, or copying of this email is strictly prohibited.
You are explicitly requested to notify the sender of this email that the intended recipient was not reached.