A270817 Integers k such that (2^k - 1) + (3^k - 1) + (5^k - 1) is prime.

1, 3, 4, 9, 11, 69, 117, 449, 675, 1119, 1959, 2687, 2859, 8001, 8175, 24269, 110247

Offset: 1

Author

Altug Alkan, Mar 23 2016

Keywords

• nonn
• more

Comments

Inspired by A268067.

Corresponding primes are 7, 157, 719, 1973317, 49007317, ...

Examples

			4 is a term because (2^4 - 1) + (3^4 - 1) + (5^4 - 1) = 719 is a prime number.
		

Crossrefs

Cf. A268064, A268067.

Programs

Mathematica

Select[Range@ 3000, PrimeQ[(2^# - 1) + (3^# - 1) + (5^# - 1)] &] (* Michael De Vlieger, Mar 23 2016 *)

PARI

lista(nn) = for(n=1, nn, if(ispseudoprime(-3 + 2^n + 3^n + 5^n), print1(n, ", ")));

Python

from sympy import isprime
def afind(limit, startk=1):
    pow2, pow3, pow5 = 2**startk, 3**startk, 5**startk
    for k in range(startk, limit+1):
        if isprime(pow2 + pow3 + pow5 - 3): print(k, end=", ")
        pow2 *= 2; pow3 *= 3; pow5 *= 5
afind(1200) # Michael S. Branicky, Sep 08 2021

Extensions

a(14)-a(15) from Michael S. Branicky, Sep 08 2021

a(16) from Michael S. Branicky, Apr 13 2023

a(17) from Michael S. Branicky, Nov 27 2024