A352083 Numbers k such that (3^k - k^3)/2 is prime.

5, 13, 205, 409, 413, 545, 88649

Offset: 1

Author

Brennan G. Benfield, Mar 03 2022

Keywords

• nonn
• more

Comments

All terms must be odd. - Michael S. Branicky, Mar 03 2022

No further terms less than 25000. - Michael S. Branicky, Mar 04 2022

Examples

			5 is a term since (3^5 - 5^3)/2 = 59 is prime.
		

Programs

Mathematica

Select[Range[1, 600, 2], PrimeQ[(3^# - #^3)/2] &] (* Amiram Eldar, Mar 03 2022 *)

PARI

isok(k) = if (denominator(x=(3^k-k^3)/2) == 1, ispseudoprime(x)); \\ Michel Marcus, Mar 03 2022

Python

from sympy import isprime
def afind(limit):
    for k in range(1, limit+1, 2):
        if isprime((3**k - k**3)//2):
            print(k, end=", ")
afind(1000) # Michael S. Branicky, Mar 03 2022

Sage

for n in srange(1,10000):
             if ((3^n-n^3)//2).is_prime():
                  print(n)

Extensions

a(7) from Michael S. Branicky, Oct 03 2024