

A100330


Positive integers n such that n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 is prime.


37



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
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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 N1 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(n1)+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: A064725 A301761 A253644 * A331043 A020473 A098833
Adjacent sequences: A100327 A100328 A100329 * A100331 A100332 A100333


KEYWORD

nonn


AUTHOR

Ray G. Opao, Nov 16 2004


STATUS

approved



