A328784 - OEIS

%I #34 Sep 08 2022 08:46:24

%S 2,4,5,608,1221,60264,205965,994856,69709961,3140421767

%N Integers k such that the k-th prime divides the k-th Lucas number.

%p a:= 1:

%p b:= 2:

%p p:= 2:

%p Res:= NULL:

%p for n from 2 to 10^6 do

%p   c:= a+b;

%p   b:= a;

%p   a:= c;

%p   p:= nextprime(p);

%p   if a mod p = 0 then

%p     Res:= Res,n;

%p   fi

%p od:

%p Res; # _Robert Israel_, Oct 30 2019

%o (Magma) [n: n in [1..100000] | IsZero(Lucas(n) mod NthPrime(n))];

%Y Cf. A000032, A000040.

%Y Cf. A075702 (analog with Fibonacci).

%K nonn,more

%O 1,1

%A _Juri-Stepan Gerasimov_, Oct 30 2019

%E a(8) from _Robert Israel_, Oct 30 2019

%E a(9)-a(10) from _Daniel Suteu_, Nov 07 2019