A255500 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.

352, 9909, 698125, 12045817, 584190541, 2487920149, 25846158097, 68520305701, 367691205289, 2846113596901, 5135516500321, 24650159312557, 61346708983561, 93685639700269, 206700247118737, 602622774810109, 1567842813615901, 2110866318916741, 4876836410298997

Offset: 1

Author

N. J. A. Sloane, Mar 13 2015

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• L. Kaylor and D. Offner, Counting matrices over a finite field with all eigenvalues in the field, Involve, a Journal of Mathematics, Vol. 7 (2014), No. 5, 627-645. [DOI]

Crossrefs

Cf. A229738, A229740, A255501.

Programs

Mathematica

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

Python

from _future_ import division
from sympy import prime
A255500_list = []
for n in range(1,10**2):
    p = prime(n)
    A255500_list.append(p**4*(p*(p*(p*(p*(p + 5) + 4) - 1) - 5) + 2)//6)
# Chai Wah Wu, Mar 14 2015

Sage

def p(n): return nth_prime(n)
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
[A255500(n) for n in (1..30)] # G. C. Greubel, Sep 24 2021