A240507 Numbers k such that 6^k - 5^k - 4^k - 3^k - 2^k - 1 is prime.

4, 6, 12, 16, 34, 48, 68, 384, 1080, 5892, 9816, 34008, 50034, 128256

Offset: 1

Author

Derek Orr, Apr 06 2014

Keywords

• nonn
• more

Comments

a(11) > 7500.

All terms are even. - Jon Perry, Apr 12 2014

Examples

			6^4 - 5^4 - 4^4 - 3^4 - 2^4 - 1 = 317 is prime. Thus, 4 is a term.
		

Crossrefs

Cf. A147977.

Cf. A000043, A240503.

Programs

PARI

for(n=1,7500,if(ispseudoprime(6^n-5^n-4^n-3^n-2^n-1),print(n)))

Python

from sympy import isprime
def afind(limit, k0=1):
    pow6, pow5, pow4, pow3, pow2 = 6**k0, 5**k0, 4**k0, 3**k0, 2**k0
    for k in range(k0, limit+1):
        if isprime(pow6 - pow5 - pow4 - pow3 - pow2 - 1): print(k, end=", ")
        pow6 *= 6; pow5 *= 5; pow4 *= 4; pow3 *= 3; pow2 *= 2
afind(1100) # Michael S. Branicky, Aug 21 2021

Extensions

a(11) from Michael S. Branicky, Aug 21 2021

a(12)-a(13) from Michael S. Branicky, Jul 05 2024

a(14) from Michael S. Branicky, May 24 2025