[seqfan] Re: "Start a sequence at the earliest reasonable point, but no earlier."
zak seidov
zakseidov at yahoo.com
Mon Aug 16 19:54:43 CEST 2010
--- On Mon, 8/16/10, Donald Alan Morrison <donmorrison at gmail.com> wrote:
> From: Donald Alan Morrison <donmorrison at gmail.com>
> Subject: [seqfan] Re: "Start a sequence at the earliest reasonable point, but no earlier."
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Cc: njas at research.att.com
> Date: Monday, August 16, 2010, 12:37 PM
> > It is impossible to be 100%
> consistent!
>
> I agree. My first confusion with offset numbers was
> with the
> squarefree numbers. Since 1 is considered both
> squareful and
> squarefree, context means everything, even for
> definitions(!) Just
> like the complex numbers are sometimes useful, and
> sometimes just more
> to think about.
>
> The second number (after the comma) in the offset field I
> think should
> be a different field though IMHO.
>
> sage: is_square(1)
> True
> sage: is_squarefree(1)
> True
> sage: is_square(2)
> False
> sage: is_squarefree(2)
> True
>
Also,
both PARI and Mathematica consider 1 as squarefree:
PARI:
gp > issquare(1)
%1 = 1
gp > issquarefree(1)
%2 = 1
Mathematica:
<<NumberTheory`NumberTheoryFunctions`
SquareFreeQ[1]
True
Zak
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