primes = 1 mod 6: comments & potential new seq

[Maximilian Hasler]

Neil,
IMHO, the

%C A002476 -3 is a quadratic residue mod a prime p iff p is in this sequence.

is wrong here and instead belongs to A045331 (these and related sequences:
http://www.research.att.com/~njas/sequences?q=7,13,19,31,37,43,61,67).

Also, the sequence http://www.research.att.com/~njas/sequences/A045375
should have %C or %Y to related ones (cf. link above, data below):

%C A045375 Up to initial term, same as A002476 = A007645 \ {2} =
A045331 \ {2,3}.

Maximilian
PS: SeqFans, any comment concerning the potential new sequence:

%S 3,2,29,97,83,5,73,103,7,101,131,251,389
%N Least prime p such that (p+1)(p+2)=-1 mod A002476(n)

Uninteresting? (Maybe remotely related to solutions of (x³-1)(y³-1)=z²...)
Or would this be more interesting:
%S 17,41,29,97,83,263,73,103,647,101,131,251,389,233
%N Least prime p>A002476(n) such that (p+1)(p+2)=-1 mod A002476(n)

-----
For convenience, sequences referred to above:

A002476  	 	 Primes of form 6n + 1. (Formerly M4344 N1819) 		+20/62
	7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139, 151,
157, 163, 181, 193, 199, 211, 223, 229, 241, 271, 277, 283, 307, 313,
331, 337, 349, 367, 373, 379, 397, 409, 421, 433, 439, 457, 463, 487,
499, 523, 541, 547, 571, 577, 601, 607, 613, 619 (list; graph; listen)

A007645 		Cuban primes: primes of the form x^2 + xy + y^2; or: primes
of form x^2 + 3*y^2; or: primes == 0 or 1 mod 3. (Formerly M2637)
		+20/38
	3, 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139,
151, 157, 163, 181, 193, 199, 211, 223, 229, 241, 271, 277, 283, 307,
313, 331, 337, 349, 367, 373, 379, 397, 409, 421, 433, 439, 457, 463,
487, 499, 523, 541, 547, 571, 577, 601, 607, 613 (list; graph; listen)

A045375 		Primes congruent to {1, 2} mod 6. 		+20/2
	2, 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139,
151, 157, 163, 181, 193, 199, 211, 223, 229, 241, 271, 277, 283, 307,
313, 331, 337, 349, 367, 373, 379, 397, 409, 421, 433, 439, 457, 463,
487 (list; graph; listen)

A045331  	 	 Primes congruent to {1, 2, 3} mod 6; or, -3 is a square
mod p.  	 	 +20/5
	2, 3, 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139,
151, 157, 163, 181, 193, 199, 211, 223, 229, 241, 271, 277, 283, 307,
313, 331, 337, 349, 367, 373, 379, 397, 409, 421, 433, 439, 457, 463,
487, 499, 523, 541, 547, 571, 577, 601, 607, 613 (list; graph; listen)