# [seqfan] possible duplicates

Douglas McNeil mcneil at hku.hk
Sun Aug 15 13:30:29 CEST 2010

```Aren't these duplicates?

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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.)

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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).

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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

```