A317979 Numbers k such that k^4 + k^3 + k^2 + 1 is prime.

2, 4, 6, 8, 14, 22, 26, 32, 36, 54, 82, 96, 98, 108, 116, 120, 124, 132, 144, 152, 162, 164, 166, 182, 226, 240, 244, 246, 252, 254, 264, 266, 274, 276, 312, 314, 322, 328, 330, 352, 364, 368, 372, 382, 406, 410, 420, 422, 428, 430, 432, 438, 456

Offset

1,1

Comments

The numbers in the sequence are all even numbers.

For k = 11*m - 4, (k^4 + k^3 + k^2 + 1)/11 is an integer, so there is no number of the form k = 11*m - 4 in the sequence.

Links

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Example

2^4 + 2^3 + 2^2 + 1 = 29 is prime, so 2 is in the sequence.

Mathematica

Select[Range[0, 1000], PrimeQ[#^4 + #^3 + #^2 + 1] &]

Prog

(PARI) for(n=1, 1000, if(ispseudoprime(n^4 + n^3 + n^2 + 1), print1(n, ", ")))
(Magma) [n: n in [0..700] |IsPrime(n^4 + n^3 + n^2 + 1)]; // Vincenzo Librandi, Sep 08 2018

Crossrefs

Cf. A005574, A119863.

Sequence in context: A288793 A049015 A039597 * A359090 A167229 A192333

Adjacent sequences: A317976 A317977 A317978 * A317980 A317981 A317982

Keyword

nonn

Author

Jinyuan Wang, Aug 12 2018

Status

approved