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Numbers k such that 3^k + k^3 is prime.
2

%I #30 Jun 27 2023 17:17:21

%S 2,56,10112,63880,78296,125330,222748,1839730

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

%C All terms == 2 or 4 mod 6. - _Robert Israel_, Jan 01 2015

%e 2 is in the sequence because 3^2 + 2^3 = 17 is prime.

%e 56 is in the sequence because 3^56 + 56^3 = 523347633027360537213687137 is prime.

%p select(t -> isprime(3^t+t^3), [seq(seq(6*i+j, j=[2,4]), i=0..100)]); # _Robert Israel_, Jan 01 2015

%t Do[If[PrimeQ[3^n+n^3], Print[n]], {n, 0, 12000}]

%o (PARI) is(n)=ispseudoprime(3^n+n^3) \\ _Charles R Greathouse IV_, Jun 06 2017

%Y Cf. A001585 (3^n + n^3), A064539 (2^n + n^2 is prime), A094133 (Leyland primes).

%K nonn,hard,more

%O 1,1

%A _Michel Lagneau_, Jan 01 2015

%E a(4)-a(7) from _Hans Havermann_, Apr 30 2015

%E a(8) from _Ryan Propper_, Jun 27 2023