A160773 Numbers k such that 3^k + 5^k + 7^k is prime.

0, 2, 10, 14, 24, 26, 126, 514, 522, 1658, 13758, 77194

Offset: 1

Author

Joao Carlos Leandro da Silva (zxawyh66(AT)yahoo.com), May 26 2009, Jun 01 2009

Keywords

• nice
• nonn
• more

Comments

Note that k must be even.

a(13) > 10^5. - Michael S. Branicky, Dec 14 2024

Examples

			For k=2 we obtain f(2) = 3^2 + 5^2 + 7^2 = 83 which is a prime.
		

References

• Joao Carlos Leandro da Silva, The Rainbow of Primes, Freund Publishing House, Tel Aviv, 2009.

Programs

Maple

A160773:=n->`if`(isprime(3^n+5^n+7^n),n,NULL): seq(A160773(n), n=0..1000); # Wesley Ivan Hurt, Sep 19 2014

Mathematica

Select[Range[0, 1000], PrimeQ[3^# + 5^# + 7^#] &] (* Wesley Ivan Hurt, Sep 19 2014 *)

PARI

isok(n) = isprime(3^n + 5^n + 7^n) \\ Michel Marcus, Jul 25 2013

Python

from itertools import count, islice
from sympy import isprime
def A160773_gen(): # generator of terms
    p3, p5, p7 = [1]*3
    for k in count(0):
        if isprime(p3+p5+p7): yield k
        p3 *= 3
        p5 *= 5
        p7 *= 7
A160773_list = list(islice(A160773_gen(),6)) # Chai Wah Wu, Dec 27 2021

Extensions

Zero added by Zak Seidov, Oct 10 2009