# [seqfan] Re: editing question

T. D. Noe noe at sspectra.com
Tue May 11 16:37:08 CEST 2010

```I think you are right; there are way too many examples.  The name needs
correcting also.  I suggest: "Primes p such that the difference q - p^2 is
a square, where q is the next prime after p^2.", but there are other
possibilities. Here is some Mma code:

Select[Prime[Range[100]], IntegerQ[Sqrt[NextPrime[#^2] - #^2]] &]

which produces

2, 5, 7, 13, 17, 37, 47, 67, 73, 97, 103, 137, 163, 167, 193, 233, 277,
281, 293, 307, 313, 317, 347, 373, 389, 421, 439, 461, 463, 487, 499, 503,
547, 571, 577, 593, 607, 613, 661, 677, 691, 701, 739, 743, 769, 787, 821,
823, 827, 829, 853, 883, 953, 967, 983, 997, 1031, 1087, 1109, 1117, 1123,
1181

Tony

At 2:21 PM +0800 5/11/10, Douglas McNeil wrote:
>(1) What's the policy on long lists in comments?  For example (abbreviated):
>
>%S A176983
>2,5,7,13,17,37,47,67,73,103,137,163,167,193,233,281,293,313,317,347,
>%T A176983 373,389,421,439,461,463,487,499,503,547
>%N A176983 Primes p such that smallest prime q > p^2 is of form q = p^2+n^2.
>%C A176983 Fermat's theorem asserts that an odd prime q can be
>expressed (uniquely) as sum of two squares:
>%C A176983 q = p^2 + n^2 with integers p and n if and only if q is
>congruent to 1 (mod 4), i.e. Pythagorean primes
>%C A176983 Square of each prime p is congruent to 1 (mod 4) as p = 4 *
>k + 1 or p = 4 * k + 3
>%C A176983 List of p^2+n^2=q
>%C A176983 2^2+1^2=5, 5^2+2^2=29, 7^2+2^2=53, 13^2+2^2=173, 17^2+2^2=293,
>%C A176983 37^2+2^2=1373, 47^2+2^2=2213, 67^2+2^2=4493, 73^2+2^2=5333,
>103^2+2^2=10613,
>%C A176983 137^2+2^2=18773, 163^2+2^2=26573, 167^2+2^2=27893,
>193^2+2^2=37253, 233^2 +2^2=54293,
>%C A176983 281^2+4^2=78977, 293^2 +2^2=85853, 313^2 +2^2=97973, 317^2
>+2^2=100493, 347^2 +2^2=120413,
>%C A176983 373^2 +2^2=139133, 389^2+4^2=151337, 421^2+4^2=177257,
>439^2+4^2=192737, 461^2+6^2=212557,
>%C A176983 463^2+2^2=214373, 487^2+2^2=237173, 499^2+4^2=249017,
>503^2+2^2=253013, 547^2+2^2=299213
>%e A176983 2^2+1^2=5=prime(3), 2=prime(1) is 1st term, trivially the
>only with n=1
>%e A176983 281^2+4^2=78977=prime(7744), 281=prime(60) is (4^2)th term,
>first with n=4
>%e A176983 461^2+6^2=212557=prime(19013), 461=prime(89) is (5^2)th
>term, first with n=6
>
>There are several terms missing and I was going to add them (and
>correct the indices in the examples), but then I realized for
>consistency I'd have to add the decompositions to the list, and I
>don't see the point of the list in the first place.
>
>If a sequence is hard, and the specifics involved in generating a term
>are hard to reproduce that's one thing; if the sequence is short and
>finite and so you can say everything there is to say with such a list,
>maybe that's another.  But when it takes more time to type in the
>one-liner which will reproduce it than it does to execute it, I don't
>really get it.  But I don't like to remove someone else's work unless
>it's manifestly wrong.
>
>(2) Is there any interest in combining the handful of OEIS classic
>documents and folk wisdom of the mailing list into an informal style
>guide?  No guide could cover all cases, and there are always reasons
>to break standards (practicality beats purity, as they say), but a
>
>of, and ways to spell..
>
>
>Doug
>
>--
>Department of Earth Sciences
>University of Hong Kong
>
>
>_______________________________________________
>
>Seqfan Mailing list - http://list.seqfan.eu/

--

Tony Noe                  | voice:     503-690-2099
Software Spectra, Inc.    | fax:       503-690-8159
14025 N.W. Harvest Lane   | e-mail:    noe at sspectra.com
Portland, OR  97229, USA  | Web site:  http://www.sspectra.com

```