# [seqfan] Re: Definition of A166980, quadratic residues

zak seidov zakseidov at yahoo.com
Mon Nov 2 16:08:05 CET 2009

```My first 120 terms of A166980:

7,11,11,19,19,17,19,31,29,53,41,41,43,53,53,59,67,73,73,73,79,89,103,97,101,107,127,127,113,127,139,139,139,151,173,163,167,173,173,179,193,193,193,197,223,211,223,241,251,233,241,241,251,283,283,269,283,281,281,283,293,307,313,313,317,353,337,349,367,353,383,389,379,383,401,389,409,401,409,419,443,433,433,439,449,457,457,461,467,487,487,509,499,499,521,509,523,523,571,557,557,563,571,571,577,593,607,601,601,607,619,617,619,631,641,643,653,653,659,673

First 80 terms coincide with RM's.

Zak

--- On Mon, 11/2/09, franktaw at netscape.net <franktaw at netscape.net> wrote:

> From: franktaw at netscape.net <franktaw at netscape.net>
> Subject: [seqfan] Re: Definition of A166980, quadratic residues
> To: seqfan at list.seqfan.eu, njas at research.att.com
> Date: Monday, November 2, 2009, 8:33 AM
> Richard,
>
> I think your second suggestion and program is the intended
>
> interpretation, and the differences are errors.  I
> recommend that you
> go ahead and edit it on that basis.
>
> Here's a PARI program if you want to include that, too:
>
> a(n)=local(p,q);q=p=prime(n);while(!issquare(Mod(p,q=nextprime(q+1))),0);
> q
>
> Neil,
>
> I note that most of this author's sequences are either
> marked "uned" or
> have been edited; the remainder mostly need
> editing.   I recommend that
> he be added to the list of those whose sequences are
> automatically
> marked "uned" if this has not already been done.
>
>
> -----Original Message-----
> From: Richard Mathar <mathar at strw.leidenuniv.nl>
>
> I do not understand the construction of A166980
> http://research.att.com/~njas/sequences/A166980
> The definition, as I see it, is that "a(n) is the smallest
> prime q
> which has a
> ...
>
> When the definition is changed to "a(n) is the smallest
> prime >
> prime(n) with
> we have
>
> A166980 := proc(n)
>         local p,q,i ;
>         p := ithprime(n) ;
>         for i from 1 do
>                 q
> := ithprime(i) ;
>                 if
> numtheory[legendre](p,q) = 1 and q>p then
>
>         return q;
>                 end
> if;
>         od:
> end proc;
> seq(A166980(n),n=1..80) ;
>
> and get
>
> 7, 11, 11, 19, 19, 17, 19, 31, 29, 53, 41, 41, 43, 53, 53,
> 59, 67, 73,
> 73, 73,
>      79, 89, 103, 97, 101, 107, 127,
> 127, 113, 127, 139, 139, 139, 151,
> 173,
>      163, 167, 173, 173, 179, 193, 193,
> 193, 197, 223, 211, 223, 241,
> 251, 233,
>      241, 241, 251, 283, 283, 269, 283,
> 281, 281, 283, 293, 307, 313,
> 313, 317,
>      353, 337, 349, 367, 353, 383, 389,
> 379, 383, 401, 389, 409, 401,
> 409, 419
> which also differs from the current A166980.
>
> Richard Mathar
>
>
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>

```