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Numbers k such that 3^k + 5^k + 7^k is prime.
4

%I #19 Dec 27 2021 13:15:13

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

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

%C Note that k must be even.

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

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

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

%t Select[Range[0, 1000], PrimeQ[3^# + 5^# + 7^#] &] (* _Wesley Ivan Hurt_, Sep 19 2014 *)

%o (PARI) isok(n) = isprime(3^n + 5^n + 7^n) \\ _Michel Marcus_, Jul 25 2013

%o (Python)

%o def A160773_gen(): # generator of terms

%o p3, p5, p7 = [1]*3

%o for k in count(0):

%o if isprime(p3+p5+p7): yield k

%o p3 *= 3

%o p5 *= 5

%o p7 *= 7

%o A160773_list = list(islice(A160773_gen(),6)) # _Chai Wah Wu_, Dec 27 2021

%K nice,nonn,more

%O 1,2

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

%E Zero added by _Zak Seidov_, Oct 10 2009