A281315 Number of 2 X 2 matrices with all elements in {0,...,n} and prime determinant.

0, 0, 13, 46, 83, 191, 272, 509, 687, 1010, 1291, 2019, 2364, 3468, 4132, 5079, 6072, 8298, 9234, 12189, 13621, 15984, 18095, 22965, 24886, 29942, 33248, 38385, 42073, 51053, 53882, 64609, 70619, 78663, 85424, 96024, 101521, 118804, 127940, 140598, 149375, 172123, 179424, 205334, 218216

Offset

0,3

Links

Chai Wah Wu, Table of n, a(n) for n = 0..1000 (terms 0..186 from Indranil Ghosh)

Example

For n = 3, a few of the possible matrices are [1,0;3,3], [1,1;0,2], [1,1;0,3], [1,1;1,3], [1,2;0,2], [1,2;0,3], [1,3;0,2], [1,3;0,3], [2,0;0,1], [2,0;1,1], [2,0;2,1], [2,0;3,1], [2,1;0,1], [2,1;1,2], [2,1;1,3], [3,1;3,2], [3,2;0,1], [3,2;1,3], [3,2;2,2], [3,2;2,3], ... There are 46 possibilities.
Here each of the matrices M is defined as M = [a,b;c,d], where a= M[1][1], b = M[1][2], c = M[2][1] and d = M[2][2]. So, a(3) = 46.

Prog

(Python)
from sympy import isprime
def t(n):
    s=0
    for a in range(n+1):
        for d in range(n+1):
            ad = a * d
            for c in range(n+1):
                for b in range(n+1):
                    if isprime(ad-b*c):
                        s+=1
    return s
for i in range(187):
    print(str(i)+" "+str(t(i)))
(Sage)
def A281315(n):
    T = Tuples([i for i in range(n+1)], 4); i = 0
    for t in T: i += is_prime(t[0]*t[3]-t[1]*t[2])
    return i
[A281315(n) for n in range(20)] # Peter Luschny, Jul 23 2017

Crossrefs

Cf. A210000.

Sequence in context: A141549 A121964 A147208 * A361622 A010003 A007587

Adjacent sequences: A281312 A281313 A281314 * A281316 A281317 A281318

Keyword

nonn

Author

Indranil Ghosh, Jan 20 2017

Status

approved