A217090 Optimus primes.

5, 7, 11, 13, 17, 19, 29, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 139, 149, 151, 157, 163, 167, 173, 179, 181, 193, 197, 199, 211, 223, 227, 229, 233, 241, 251, 257, 263, 269, 271, 281, 283, 293, 307, 311, 313

Offset

1,1

Comments

An odd prime p is an optimus prime if (1 + sqrt(Legendre(-1, p)*p))^p - 1 = a + b*sqrt(Legendre(-1, p)*p), where gcd(a, b) = p.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Arkadii Slinko, Additive Representability of Finite Measurement Structures, 2007, 26 pp.

Arkadii Slinko, Additive Representability of Finite Measurement Structures, 2007, 26 pp. [Cached copy, permission requested]

Prog

(PARI) is(p)=if(p<3 || !isprime(p), return(0)); my(t=(2*quadgen(kronecker(-1, p)*p))^p); gcd(imag(t), real(t)-1)==p \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

Cf. A138465 (non-Optimus primes).

Sequence in context: A093496 A171688 A239711 * A253969 A191056 A314296

Adjacent sequences: A217087 A217088 A217089 * A217091 A217092 A217093

Keyword

nonn

Author

Arkadiusz Wesolowski, Sep 26 2012

Status

approved