they were associated with a Calabi-Yau based L-function in

a paper with no real good definition.

So I did a web search and an OEIS search and some experimentation.

A little thought of the geometric average basis of the defintion gave

me an higher order "bad" I call "worse".

An a good I call "Angel".

%I A000001

%S A000001 19, 43, 47, 61, 73, 79, 83, 89, 109, 113, 137, 139, 157,

167, 181, 197, 199,

211, 229, 233, 239, 241, 271, 281, 283, 293, 313, 317, 353, 359, 383, 389,

401, 439, 443, 449, 463, 467, 503, 509, 521, 523

%N A000001 Worse primes<-bad primes (A130903):

If[Prime[n]^2 - Prime[n + 2]*Prime[n - 2] < 0,

Prime[n]]

%F A000001 a(n) = If[Prime[n]^2 - Prime[n + 2]*Prime[n - 2] < 0,

Prime[n]]

%t A000001 Flatten[Table[If[Prime[n]^2 - Prime[n + 2]*Prime[n - 2]

< 0,Prime[n], {}], {n, 3, 100}]]

%Y A000001 Cf. A130903

%O A000001 1

%K A000001 ,nonn,

%A A000001 Roger Bagula and Gary W. Adamsom (rlbagulatftn@...),

May 23 2008

RH

RA 192.20.225.32

RU

RI

%I A000001

%S A000001 5, 7, 11, 13, 17, 23, 29, 31, 37, 41, 53, 59, 67, 71, 97,

101, 103, 107,

127, 131, 149, 151, 163, 173, 179, 191, 193, 223, 227, 251, 257, 263, 269,

277, 307, 311, 331, 337, 347, 349, 367, 373, 379, 397, 409, 419, 421, 431,

433, 457, 461, 479, 487, 491, 499, 541

%N A000001 Angel primes<-good primes (A028388):

If[Prime[n]^2 - Prime[n + 2]*Prime[n - 2] > 0,

Prime[n]]

%C A000001 This sequence set is a next level higher of good and bad

primes.

The bad primes come from modular forms and L-Series theory.

http://en.wikipedia.org/wiki/Arithmetic_of_elliptic_curves:

Quote:

"Reduction mod p

Reduction of an abelian variety A modulo a prime ideal of (the

integers of) K - say, a prime number p - to get an abelian variety Ap

over a finite field, is possible for almost all p. The 'bad' primes,

for which the reduction degenerates by acquiring singular points, are

known to reveal very interesting information. As often happens in

number theory, the 'bad' primes play a rather active role in the theory.

Here a refined theory of (in effect) a right adjoint to reduction mod

p - the NÃ©ron model - cannot always be avoided. In the case of an

elliptic curve there is an algorithm of John Tate describing it.

For abelian varieties such as Ap, there is a definition of local

zeta-function available. To get an L-function for A itself, one takes

a suitable Euler product of such local functions; to understand the

finite number of factors for the 'bad' primes one has to refer to the

Tate module of A, which is (dual to) the Ã©tale cohomology group

H1(A), and the Galois group action on it. In this way one gets a

respectable definition of Hasse-Weil L-function for A. In general its

properties, such as functional equation, are still conjectural - the

Taniyama-Shimura conjecture was just a special case, so that's hardly

surprising.

It is in terms of this L-function that the conjecture of Birch and

Swinnerton-Dyer is posed. It is just one particularly interesting

aspect of the general theory about values of L-functions L(s) at

integer values of s, and there is much empirical evidence supporting it."

%D A000001 http://en.wikipedia.org/wiki/Arithmetic_of_elliptic_curves

%F A000001 a(n) = If[Prime[n]^2 - Prime[n + 2]*Prime[n - 2] <>0,

Prime[n]]

%t A000001 Flatten[Table[If[Prime[n]^2 - Prime[n + 2]*Prime[n - 2]> 0,Prime[n], {}], {n, 3, 100}]]

%Y A000001 Cf. A130903,A028388

%O A000001 1

%K A000001 ,nonn,

%A A000001 Roger Bagula and Gary W. Adamsom (rlbagulatftn@...),

May 23 2008

RH

RA 192.20.225.32

RU

RI

--

Respectfully, Roger L. Bagula

11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814

:http://www.geocities.com/rlbagulatftn/Index.html

alternative email: rlbagula@...