A228227 Primes congruent to {7, 11} mod 16.

7, 11, 23, 43, 59, 71, 103, 107, 139, 151, 167, 199, 251, 263, 283, 311, 331, 347, 359, 379, 439, 443, 487, 491, 503, 523, 571, 587, 599, 619, 631, 647, 683, 727, 743, 811, 823, 827, 839, 859, 887, 907, 919, 967, 971, 983, 1019, 1031, 1051, 1063, 1163, 1223

Offset: 1

Author

Arkadiusz Wesolowski, Aug 16 2013

Keywords

• nonn

Comments

Union of A141194 and A141195.

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. Therefore A060953(a(n)) = 0.

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, A141194, A141195, A228228.

Programs

Magma

[p: p in PrimesUpTo(1223) | p mod 16 in {7, 11}];

Mathematica

Select[Prime@Range[200], MemberQ[{7, 11}, Mod[#, 16]] &]