[seqfan] Re: A047210: First term and offset(?)

[franktaw at netscape.net]

Several points here:

First, there is no reason why the sequence in the OEIS needs to match 
the one in
MathWorld for initial values and offsets.

I don't know exactly why Eric left n=1 out of his description, but 
possible reasons
include the fact that the integers mod 1 aren't very interesting, and 
that the
sequence consists entirely of strictly positive integers without it.

Regardless of the above, there are very good reasons for including the 
case n=1
in the OEIS.  The main one is because of the way the OEIS is searched.  
Someone
searching for the sequence is likely to look for either 
"1,1,1,4,4,4,7,9,9,9,12,11"
or "0,1,1,1,4,4,4,7,9,9,9,12,11" (amongst numerous other 
possibilities).  With the
sequence as it is, either search will succeed.  If the initial 0 was 
removed, the
second would fail.

(As others have noted, it is also the case that the definition applies 
perfectly well
to n=1, with a(1) = 0 as the correct value.  There is thus no good 
reason to
omit it.)

This is the flip side of the advice on the lookup hints page to "leave 
off the first
term or two, because people may disagree about where the sequence 
begins."
When entering a sequence, generally include initial terms that could 
reasonably be
omitted.  This even applies to some sequences like A006530 (largest 
prime factor
of n), where the sequence really "should" be undefined at n=1.

If you are submitting a sequence and are uncertain whether it should be 
defined
at n=1 and/or n=0 -- and what the value(s) there should be -- this is a 
good
question to ask on this mailing list.

Franklin T. Adams-Watters

-----Original Message-----
From: zak seidov <zakseidov at yahoo.com>

Dear seqfans,

i'm confused with Eric's description of A047210 and
entries/offset in  A047210...

One way out to edit A047210 in accord with Eric is:

1. to omit first zero from %S, and
2. to change offset to 2

thx, zak


Eric writes:
The largest quadratic residues for p=2, 3, ... are 1, 1, 1, 4, 4, 4, 4, 
7, 9, 9,
9, 12, 11, ... (Sloane's A047210).

%I A047210
%S A047210 
0,1,1,1,4,4,4,4,7,9,9,9,12,11,10,9,16,16,17,16,18,20,18,16,24,25,25,
%T A047210 
25,28,25,28,25,31,33,30,28,36,36,36,36,40,39,41,37,40,41,42,36,46,49,
%U A047210 
49,49,52,52,49,49,55,57,57,49,60,59,58,57,64,64,65,64,64,65,64,64,72
%N A047210 Largest square modulo n.
%H A047210 Eric Weisstein's World of Mathematics, <a 
href="http://mathworld.wolfram.com/
               QuadraticResidue.html">Quadratic Residue</a>
%Y A047210 Adjacent sequences: A047207 A047208 A047209 this_sequence 
A047211
A047212
               A047213
%Y A047210 Sequence in context: A111655 A113646 A106325 this_sequence 
A120327
A056629
               A081676
%K A047210 easy,nonn
%O A047210 0,5
%A A047210 Henry Bottomley (se16(AT)btinternet.com), Jun 08 2000

Eric writes:
http://mathworld.wolfram.com/QuadraticResidue.html
The largest quadratic residues for p=2, 3, ... are 1, 1, 1, 4, 4, 4, 4, 
7, 9, 9,
9, 12, 11, ... (Sloane's A047210).