

A217090


Optimus primes.


3



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
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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 (nonOptimus 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



