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

franktaw at netscape.net franktaw at netscape.net
Thu Dec 18 21:54:32 CET 2008

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.  
searching for the sequence is likely to look for either 
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 
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 
at n=1 and/or n=0 -- and what the value(s) there should be -- this is a 
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 
%T A047210 
%U A047210 
%N A047210 Largest square modulo n.
%H A047210 Eric Weisstein's World of Mathematics, <a 
               QuadraticResidue.html">Quadratic Residue</a>
%Y A047210 Adjacent sequences: A047207 A047208 A047209 this_sequence 
%Y A047210 Sequence in context: A111655 A113646 A106325 this_sequence 
%K A047210 easy,nonn
%O A047210 0,5
%A A047210 Henry Bottomley (se16(AT)btinternet.com), Jun 08 2000

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).

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