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A237364 Numbers n of the form n=Phi(7,p) (for prime p) such that Phi(7,n) is also prime. 1
616067011, 58749951412747, 93054242152309543, 146945091162352770847, 2224989620406870255043, 43184085337135904888293, 53224134341571172990843, 109539169818149034933067, 308295173856880401026941, 6197901576526752380316343, 14789135287218506962379317 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..11.

EXAMPLE

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.

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

PROG

(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)}

CROSSREFS

Cf. A088550.

Sequence in context: A236948 A184216 A123705 * A251498 A233848 A018786

Adjacent sequences:  A237361 A237362 A237363 * A237365 A237366 A237367

KEYWORD

nonn

AUTHOR

Derek Orr, Feb 06 2014

STATUS

approved

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Last modified June 20 19:36 EDT 2019. Contains 324234 sequences. (Running on oeis4.)