A237364 Numbers n of the form n=Phi(7,p) (for prime p) such that Phi(7,n) is also prime.

616067011, 58749951412747, 93054242152309543, 146945091162352770847, 2224989620406870255043, 43184085337135904888293, 53224134341571172990843, 109539169818149034933067, 308295173856880401026941, 6197901576526752380316343, 14789135287218506962379317

Offset: 1

Author

Derek Orr, Feb 06 2014

Keywords

• nonn

Comments

Phi(7,x) =1+x+x^2+x^3+x^4+x^5+x^6 =A053716(x) is the 7th cyclotomic polynomial.

Examples

			616067011 = 29^6+29^5+29^4+29^3+29^2+29+1 (29 is prime) and 616067011^6+616067011^5+616067011^4+616067011^3+616067011^2+616067011+1 = 54672347801779330810964871392077416495507203132755717 is prime. Thus, 616067011 is a member of this sequence.
		

Crossrefs

Cf. A088550.

Programs

Maple

for k from 1 do
    p := ithprime(k) ;
    n := numtheory[cyclotomic](7,p) ;
    pn := numtheory[cyclotomic](7,n) ;
    if isprime( pn) then
        print(n) ;
    end if;
end do: # R. J. Mathar, Feb 07 2014

Python

import sympy
from sympy import isprime
{print(n**6+n**5+n**4+n**3+n**2+n+1) for n in range(10**5) if isprime(n) and isprime((n**6+n**5+n**4+n**3+n**2+n+1)**6+(n**6+n**5+n**4+n**3+n**2+n+1)**5+(n**6+n**5+n**4+n**3+n**2+n+1)**4+(n**6+n**5+n**4+n**3+n**2+n+1)**3+(n**6+n**5+n**4+n**3+n**2+n+1)**2+(n**6+n**5+n**4+n**3+n**2+n+1)+1)}