A228228 Primes congruent to {3, 5, 13, 15} mod 16.

3, 5, 13, 19, 29, 31, 37, 47, 53, 61, 67, 79, 83, 101, 109, 127, 131, 149, 157, 163, 173, 179, 181, 191, 197, 211, 223, 227, 229, 239, 269, 271, 277, 293, 307, 317, 349, 367, 373, 383, 389, 397, 419, 421, 431, 461, 463, 467, 479, 499, 509, 541, 547, 557, 563

Offset

1,1

Comments

Union of A091968, A127589, A141196, and A127576.

Let p be a prime number and let E(p) denote the elliptic curve y^2 = x^3 + p*x. If p is in the sequence, then the rank of E(p) is 0 or 1. Therefore, A060953(a(n)) must be one of only two values: 0 or 1.

References

J. H. Silverman, The arithmetic of elliptic curves, Springer, NY, 1986, p. 311.

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000

Mathematica

Select[Prime@Range[103], MemberQ[{3, 5, 13, 15}, Mod[#, 16]] &]

Prog

(Magma) [p: p in PrimesUpTo(563) | p mod 16 in {3, 5, 13, 15}]

Crossrefs

Cf. A007519, A060953, A091968, A127576, A127589, A141196, A228227.

Sequence in context: A136053 A157468 A191017 * A227031 A157974 A019420

Adjacent sequences: A228225 A228226 A228227 * A228229 A228230 A228231

Keyword

nonn

Author

Arkadiusz Wesolowski, Aug 16 2013

Status

approved