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

Author

Arkadiusz Wesolowski, Aug 16 2013

Keywords

• nonn

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

Crossrefs

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

Programs

Magma

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

Mathematica

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