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A120480
Primes of the form k^5 + k^2 + 1.
4
3, 37, 32833, 3200401, 14349637, 52523101, 130692997, 254806273, 459167941, 2706790087, 3486790963, 3939047533, 10510110703, 12762826651, 14025528757, 14693292433, 16850593873, 23863550761, 34359754753, 38579506813
OFFSET
1,1
COMMENTS
The values of k such that k^5 + k^2 + 1 is prime are 1, 2, 8, 20, 27, 35, 42, 48, 54, 77, 81, 83, 101, 105, 107, 108, 111, 119, 128, 131. Little is known about primality in quintic forms.
LINKS
EXAMPLE
a(1) = 3 = 1^5 + 1^2 + 1.
a(2) = 37 = 2^5 + 2^2 + 1.
a(3) = 132833 = 8^5 + 8^2 + 1.
a(4) = 3200401 = 20^5 + 20^2 + 1.
MATHEMATICA
Select[Table[k^5+k^2+1, {k, 150}], PrimeQ] (* Harvey P. Dale, Oct 29 2020 *)
PROG
(Magma) [a: n in [0..160] | IsPrime(a) where a is n^5+n^2+1 ]; // Vincenzo Librandi, Dec 22 2010
CROSSREFS
Cf. A000040.
Sequence in context: A351759 A132931 A172029 * A088098 A284411 A176245
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jul 21 2006
STATUS
approved