A255500 - OEIS

%I #26 Sep 26 2021 13:13:41

%S 352,9909,698125,12045817,584190541,2487920149,25846158097,

%T 68520305701,367691205289,2846113596901,5135516500321,24650159312557,

%U 61346708983561,93685639700269,206700247118737,602622774810109,1567842813615901,2110866318916741,4876836410298997

%N a(n) = (p^9 + 5*p^8 + 4*p^7 - p^6 - 5*p^5 + 2*p^4)/6 where p is the n-th prime.

%H G. C. Greubel, <a href="/A255500/b255500.txt">Table of n, a(n) for n = 1..1000</a>

%H L. Kaylor and D. Offner, <a href="https://projecteuclid.org/euclid.involve/1513733722">Counting matrices over a finite field with all eigenvalues in the field</a>, Involve, a Journal of Mathematics, Vol. 7 (2014), No. 5, 627-645. [<a href="http://dx.doi.org/10.2140/involve.2014.7.627">DOI</a>]

%t Table[(p^9+5p^8+4p^7-p^6-5p^5+2p^4)/6,{p,Prime[Range[20]]}] (* _Harvey P. Dale_, May 23 2020 *)

%o (Python)

%o from __future__ import division

%o from sympy import prime

%o A255500_list = []

%o for n in range(1,10**2):

%o ....p = prime(n)

%o ....A255500_list.append(p**4*(p*(p*(p*(p*(p + 5) + 4) - 1) - 5) + 2)//6)

%o # _Chai Wah Wu_, Mar 14 2015

%o (Sage)

%o def p(n): return nth_prime(n)

%o def A255500(n): return p(n)^4*(p(n)^5 +5*p(n)^4 +4*p(n)^3 -p(n)^2 -5*p(n) +2)/6

%o [A255500(n) for n in (1..30)] # _G. C. Greubel_, Sep 24 2021

%Y Cf. A229738, A229740, A255501.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Mar 13 2015