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A075715 Numbers n such that n^16 + n + 1 is prime. 4
1, 2, 21, 26, 47, 65, 99, 102, 206, 215, 216, 257, 294, 342, 437, 441, 537, 540, 702, 747, 837, 860, 909, 912, 921, 926, 942, 1020, 1071, 1101, 1112, 1125, 1181, 1254, 1266, 1322, 1344, 1364, 1370, 1406, 1422, 1665, 1814, 1821, 1829, 1905, 2024 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For s = 5, 8, 11, 14, 17, 20, ..., n_s = 1 + n + n^s is always composite for any n > 1. Also at n = 1, n_s = 3 is a prime for any s. So it is interesting to consider only the cases of s =/= 5, 8, 11, 14, 17, 20, ... and n > 1. Here we consider the case s = 16 and find several first n's making n_s a prime (or a probable prime).

LINKS

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

EXAMPLE

2 is in the sequence because 1 + 2 + 2^16 = 65539 is prime.

MAPLE

A075715:=n->if type(1+n+n^16, prime) then n; fi; seq(A075715(n), n=1..3000); # Wesley Ivan Hurt, Dec 17 2013

MATHEMATICA

Select[Range[3000], PrimeQ[#^16 + # + 1] &] (* Vincenzo Librandi, Dec 17 2013 *)

PROG

(PARI) for(n=1, 3000, if(isprime(1+n+n^16), print1(n", ")))

(MAGMA) [n: n in [1..3000]| IsPrime(n^16+n+1)]; // Vincenzo Librandi, Dec 17 2013

CROSSREFS

Cf. A002384, A075714, A075716.

Sequence in context: A135053 A042565 A079907 * A326735 A294377 A071761

Adjacent sequences:  A075712 A075713 A075714 * A075716 A075717 A075718

KEYWORD

nonn,easy

AUTHOR

Zak Seidov, Oct 03 2002

EXTENSIONS

More terms from Ralf Stephan, Mar 19 2003

STATUS

approved

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Last modified August 14 19:09 EDT 2020. Contains 336483 sequences. (Running on oeis4.)