A305415 Numbers k such that F(k)*F(k+1) - F(k+2) is prime, where F = A000045.
4, 6, 7, 8, 10, 11, 14, 25, 34, 40, 44, 54, 62, 63, 66, 108, 190, 266, 299, 306, 310, 343, 350, 638, 726, 984, 1626, 2223, 2591, 2843, 3291, 3694, 4198, 4473, 4494, 5128, 7934, 10595, 12515, 17433, 17883, 19979, 23887, 28847, 30071, 64168, 79073, 81971
Offset: 1
Keywords
Programs
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Magma
[n: n in [1..800] | IsPrime(Fibonacci(n)*Fibonacci(n+1)-Fibonacci(n+2))];
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Maple
with(combinat,fibonacci): select(n->isprime(fibonacci(n)*fibonacci(n+1)-fibonacci(n+2)),[$1..8000]); # Muniru A Asiru, Jun 12 2018
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Mathematica
Select[Range[3000], PrimeQ[(Fibonacci[#] Fibonacci[# + 1] - Fibonacci[# + 2])]&]
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PARI
isok(k) = isprime(fibonacci(k)*fibonacci(k+1) - fibonacci(k+2)); \\ Michel Marcus, Jun 13 2018
Extensions
a(38)-a(46) from Giovanni Resta, Jun 15 2018
a(47)-a(48) from Robert Price, Jun 18 2018
Comments