login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 12:26 EST 2022. Contains 358586 sequences. (Running on oeis4.)