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A317979
Numbers k such that k^4 + k^3 + k^2 + 1 is prime.
1
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
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
Sequence in context: A288793 A049015 A039597 * A359090 A167229 A192333
KEYWORD
nonn
AUTHOR
Jinyuan Wang, Aug 12 2018
STATUS
approved