login
Numbers k such that Lucas(k) + prime(k) is a prime.
1

%I #24 Sep 08 2022 08:46:19

%S 1,6,12,18,54,75,354,10158,23280,33726,38226,70749,244779,308604

%N Numbers k such that Lucas(k) + prime(k) is a prime.

%C a(15) > 500000.

%e a(1) = 1 because Lucas(1)=1, prime(1)=2 and 1+2=3 is a prime.

%e a(2) = 6 because Lucas(6)=18, prime(6)=13 and 18+13=31 is a prime.

%t Select[Range[1000], PrimeQ[LucasL[#] + Prime[#]] &]

%o (Magma) [n: n in [1..950] | IsPrime(Lucas(n)+NthPrime(n))];

%Y Cf. A000032, A000040, A050180.

%K nonn,more

%O 1,2

%A _Vincenzo Librandi_, Jun 16 2017

%E a(8)-a(12) from _Robert Price_, Oct 26 2017

%E a(13)-a(14) from _Robert Price_, Dec 16 2017