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

%I A160773 #28 Apr 28 2025 11:53:57
%S A160773 0,2,10,14,24,26,126,514,522,1658,13758,77194
%N A160773 Numbers k such that 3^k + 5^k + 7^k is prime.
%C A160773 Note that k must be even.
%C A160773 a(13) > 10^5. - _Michael S. Branicky_, Dec 14 2024
%D A160773 Joao Carlos Leandro da Silva, The Rainbow of Primes, Freund Publishing House, Tel Aviv, 2009.
%e A160773 For k=2 we obtain f(2) = 3^2 + 5^2 + 7^2 = 83 which is a prime.
%p A160773 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 A160773 Select[Range[0, 1000], PrimeQ[3^# + 5^# + 7^#] &] (* _Wesley Ivan Hurt_, Sep 19 2014 *)
%o A160773 (PARI) isok(n) = isprime(3^n + 5^n + 7^n) \\ _Michel Marcus_, Jul 25 2013
%o A160773 (Python)
%o A160773 from itertools import count, islice
%o A160773 from sympy import isprime
%o A160773 def A160773_gen(): # generator of terms
%o A160773     p3, p5, p7 = [1]*3
%o A160773     for k in count(0):
%o A160773         if isprime(p3+p5+p7): yield k
%o A160773         p3 *= 3
%o A160773         p5 *= 5
%o A160773         p7 *= 7
%o A160773 A160773_list = list(islice(A160773_gen(),6)) # _Chai Wah Wu_, Dec 27 2021
%K A160773 nice,nonn,more
%O A160773 1,2
%A A160773 Joao Carlos Leandro da Silva (zxawyh66(AT)yahoo.com), May 26 2009, Jun 01 2009
%E A160773 Zero added by _Zak Seidov_, Oct 10 2009