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A245801
Positive k such that Lucas(3*k) - Fibonacci(k) is a prime.
1
1, 2, 28, 58, 98, 118, 212, 238, 350, 478, 883, 2660, 3971, 21491, 88843
OFFSET
1,2
COMMENTS
k=0 would give the prime 2, but positive k is required. Some terms correspond to probable primes. a(15) > 40000. - Jens Kruse Andersen, Aug 04 2014
MAPLE
with(combinat): A245801:=n->`if`(isprime(fibonacci(3*n+1)+fibonacci(3*n-1)-fibonacci(n)), n, NULL): seq(A245801(n), n=1..1000); # Wesley Ivan Hurt, Aug 04 2014
MATHEMATICA
Select[Range[3000], PrimeQ[LucasL[3 #] - Fibonacci[#]] &]
PROG
(Magma) [n: n in [1..800] | IsPrime(Lucas(3*n) - Fibonacci(n))];
(Python)
import sympy
{print(n, end=', ') for n in range(10**3) if sympy.isprime(sympy.lucas(3*n)-sympy.fibonacci(n))} # Derek Orr, Aug 03 2014
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Vincenzo Librandi, Aug 02 2014
EXTENSIONS
a(14) from Jens Kruse Andersen, Aug 04 2014
a(15) from Michael S. Branicky, Oct 26 2024
STATUS
approved