[seqfan] Re: possible duplicates

Charles Greathouse charles.greathouse at case.edu
Sun Aug 15 18:00:58 CEST 2010

```I agree, these all look like duplicates.  The first pairs certainly
are, and should have their doppelgängers removed.

The last pair, I think, is the union of A040117 and A068229: primes
that are ±5 mod 12.  So we have a lot of alternate descriptions that
should go in the sequence:
1. (Rational) primes that don't split over Q[sqrt(3)]
2. Primes that are ±5 mod 12
3. Primes p such that 3 is not a square mod p
4. Odd primes p such that p divides 3^((p-1)/2) + 1

Anyone want to check that I haven't made any mistakes?  /Pro forma/, I
tested that #2, #3, and #4 correspond up to 10^9; my understanding of
#1 is that this occurs when Legendre(12 / p) = -1, and this happens
precisely when #2 is true.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Sun, Aug 15, 2010 at 7:30 AM, Douglas McNeil <mcneil at hku.hk> wrote:
> Aren't these duplicates?
>
> --
>
> http://oeis.org/classic/?q=id%3AA140433|id%3AA155934
>
> A140433                 Primes of the form (n+0)^0+(n+1)^1+(n+2)^2+(n+3)^3+(n+4)^4.
>        701, 2647, 3381, 7129, 15731, 53551, 110161, 405001, 473201, 549667
>
> A155934                  Primes of the form : n^0+(n+1)^1+(n+2)^2+(n+3)^3+(n+4)^4.
>        701, 2647, 4481, 7129, 15731, 53551, 110161, 405001, 473201, 549667,
> 1079297, 1541051, 1922077, 6892651, 8654689, 10734697, 13168801,
> 15995071, 30380849, 33789601, 55322081, 72401057, 85800961, 113622391,
> 147716801, 238297249
>
> But 3381 isn't prime.  (Came across this one when looking for
> properties of 2647 for Zak's question.)
>
> --
>
> Two word-based sequences:
>
> http://oeis.org/classic/?q=55893641747
>
> A072959                  a(n) = the name of n evaluated in base 27, using blank=0,
> hyphen=0, A=1, B=2,... Z=26.
>        515904, 11318, 15216, 10799546, 129618, 125258, 14118, 10211981,
> 2839691, 282506, 14729, 78236429, 299309045, 212445531527,
> 68884716992, 2457249197, 7503281492, 5427065792075, 55893641747,
> 150135668600, 299310469
>
> A087096                  Using the US English name for the nonnegative integers,
> assign each letter a numerical value as in A073327 (A=1, B=2, ...,
> Z=26) and treat the name as a base-27 integer. Convert to decimal.
>        515904, 11318, 15216, 10799546, 129618, 125258, 14118, 10211981,
> 2839691, 282506, 14729, 78236429, 299309045, 212445531527,
> 68884716992, 2457249197, 7503281492, 5427065792030, 55893641747,
> 150135668600, 299310469
>
> I think these are supposed to be the same sequence.  The second also
> seems wrong at 17.  I can match A072959's results, and it has a code
> posted, so I propose killing A087096 (and changing A072959's offset).
>
> --
>
> http://oeis.org/classic/index.html?q=id%3AA038875|id%3AA003630
>
> A038875                  3 is not a square mod p.
>        2, 5, 7, 17, 19, 29, 31, 41, 43, 53, 67, 79, 89, 101, 103, 113, 127,
> 137, 139, 149, 151, 163, 173, 197, 199, 211, 223, 233, 257, 269, 271,
> 281, 283, 293, 307, 317, 331, 353, 367, 379, 389, 401, 439, 449, 461,
> 463
>
> Isn't 3 a square mod 2? 3=1 mod 2, and 1 is a square.  (Maybe a "3 in
> set of squares mod p" instead of "3 mod p in set of squares mod p"
> bug, which I've made myself repeatedly.)  After removing 2, this looks
> like
>
> A003630                  Inert rational primes in Q(sqrt 3).
>        5, 7, 17, 19, 29, 31, 41, 43, 53, 67, 79, 89, 101, 103, 113, 127,
> 137, 139, 149, 151, 163, 173, 197, 199, 211, 223, 233, 257, 269, 271,
> 281, 283, 293, 307, 317, 331, 353, 367, 379, 389, 401, 439, 449, 461,
> 463, 487, 499, 509, 521, 523, 547, 557, 569, 571, 593
>
> to me but I may be misunderstanding the definition of inert.
>
> Each of the above sequences differs from its (possible) duplicate
> because of an error, which may explain why they weren't noticed at
> submission time (and why duplicate searching needs to be
> fault-tolerant).  Or maybe the errors are mine!
>
>
> Doug
>
> --
> Department of Earth Sciences
> University of Hong Kong
>
>
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>

```