A228228 - OEIS

%I #13 Sep 08 2022 08:46:05

%S 3,5,13,19,29,31,37,47,53,61,67,79,83,101,109,127,131,149,157,163,173,

%T 179,181,191,197,211,223,227,229,239,269,271,277,293,307,317,349,367,

%U 373,383,389,397,419,421,431,461,463,467,479,499,509,541,547,557,563

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

%C Union of A091968, A127589, A141196, and A127576.

%C 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.

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

%H Arkadiusz Wesolowski, <a href="/A228228/b228228.txt">Table of n, a(n) for n = 1..1000</a>

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

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

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

%K nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Aug 16 2013