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A228228
Primes congruent to {3, 5, 13, 15} mod 16.
2
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}]
KEYWORD
nonn
AUTHOR
STATUS
approved