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A100330 Positive integers n such that n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 is prime. 35
1, 2, 3, 5, 6, 13, 14, 17, 26, 31, 38, 40, 46, 56, 60, 61, 66, 68, 72, 73, 80, 87, 89, 93, 95, 115, 122, 126, 128, 146, 149, 156, 158, 160, 163, 180, 186, 192, 203, 206, 208, 220, 221, 235, 237, 238, 251, 264, 266, 280, 282, 290, 294, 300, 303, 320, 341, 349, 350 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The corresponding primes are A088550. - Bernard Schott, Dec 20 2012

n = 5978493 * 2^150006 - 1 is an example of a very large member of this sequence. The generated prime is proved by the N-1 method (because n is prime and n*(n+1) is fully factored and this provides for an exactly 33.33...% factorization for Phi_7(n) - 1). - Serge Batalov, Mar 13 2015

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

EXAMPLE

2 is in the sequence because 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2 + 1 = 127, which is prime.

MAPLE

A100330 := proc(n)

    option remember;

    local a;

    if n = 1 then

        1;

    else

        for a from procname(n-1)+1 do

            if isprime(numtheory[cyclotomic](7, a)) then

                return a;

            end if;

        end do:

    end if;

end proc:

seq(A100330(n), n=1..30) ; # R. J. Mathar, Feb 07 2014

MATHEMATICA

Select[Range[350], PrimeQ[Sum[ #^i, {i, 0, 6}]] &] (* Ray Chandler, Nov 17 2004 *)

Do[If[PrimeQ[n^6 + n^5 + n^4 + n^3 + n^2 + n + 1], Print[n]], {n, 1, 500}] (* Vincenzo Librandi, Feb 08 2014 *)

PROG

(MAGMA) [n: n in [1..500]| IsPrime(n^6 + n^5 + n^4 + n^3 + n^2 + n + 1)]; // Vincenzo Librandi, Feb 08 2014

(PARI) is(n)=isprime(polcyclo(7, n)) \\ Charles R Greathouse IV, Apr 28 2015

CROSSREFS

Cf. A100331, A250174 (Phi_14(n) = n^6 - n^5 + n^4 - n^3 + n^2 - n + 1 primes; these two sequences can also be considered an extension of each other into negative n values), A250177 (Phi_21(n) primes).

Sequence in context: A075372 A064725 A253644 * A020473 A098833 A075371

Adjacent sequences:  A100327 A100328 A100329 * A100331 A100332 A100333

KEYWORD

nonn

AUTHOR

Ray G. Opao, Nov 16 2004

STATUS

approved

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Last modified April 28 00:46 EDT 2017. Contains 285556 sequences.