A120480 Primes of the form k^5 + k^2 + 1.

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

Harvey P. Dale, Table of n, a(n) for n = 1..2000

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

Adjacent sequences: A120477 A120478 A120479 * A120481 A120482 A120483

Keyword

easy,nonn

Author

Jonathan Vos Post, Jul 21 2006

Status

approved