login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A237360 Numbers n of the form p^2+p+1 (for prime p) such that n^2+n+1 is also prime. 3
57, 381, 993, 4557, 16257, 32943, 49953, 58323, 109893, 135057, 167691, 214833, 237657, 453603, 503391, 564753, 658533, 678153, 780573, 995007, 1248807, 1516593, 1746363, 2218611, 2400951, 3465183, 3738423, 4340973, 4750221, 5232657, 6118203 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..10000

EXAMPLE

57 = 7^2+7+1 (7 is prime) and 57^2+57+1 = 3307 is also prime. Thus, 57 is a member of this sequence.

MAPLE

for k from 1 do

    p := ithprime(k) ;

    n := numtheory[cyclotomic](3, p) ;

    pn := numtheory[cyclotomic](3, n) ;

    if isprime( pn) then

        print(n) ;

    end if;

end do: # R. J. Mathar, Feb 07 2014

MATHEMATICA

Select[Table[p^2+p+1, {p, Prime[Range[500]]}], PrimeQ[#^2+#+1]&] (* Harvey P. Dale, Feb 09 2014 *)

PROG

(Python)

import sympy

from sympy import isprime

{print(n**2+n+1) for n in range(10**4) if isprime(n) and isprime((n**2+n+1)**2+(n**2+n+1)+1)}

(PARI) s=[]; forprime(p=2, 4000, if(isprime(p^4+2*p^3+4*p^2+3*p+3), s=concat(s, p^2+p+1))); s \\ Colin Barker, Feb 07 2014

CROSSREFS

Cf. A060800, A002383.

Sequence in context: A209517 A097200 A211147 * A076459 A268260 A184224

Adjacent sequences:  A237357 A237358 A237359 * A237361 A237362 A237363

KEYWORD

nonn

AUTHOR

Derek Orr, Feb 06 2014

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 20 17:27 EDT 2019. Contains 324234 sequences. (Running on oeis4.)