A271428 Values of k such that F(k)*F(k+1)-1 is a prime, where F(k) is the k-th Fibonacci number (A000045).
3, 6, 24, 42, 48, 86, 102, 138, 182, 302, 438, 506, 926, 1266, 3600, 23550, 24122, 42410, 51432, 82290, 137246
Offset: 1
Examples
6 is in the sequence because F(6)*F(7)-1 = 8*13-1 = 103, which is prime.
Programs
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Mathematica
Select[Range[5 * 10^3], PrimeQ[Fibonacci@ # Fibonacci[# + 1] - 1] &] (* Michael De Vlieger, Apr 07 2016 *)
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PARI
L=List(); for(k=1, 1000, if(ispseudoprime(fibonacci(k)*fibonacci(k+1)-1), listput(L, k))); Vec(L)
Extensions
a(15) from Michael De Vlieger, Apr 07 2016
a(16)-a(20) from Robert Price, Apr 14 2016
a(21) from Michael S. Branicky, Dec 17 2024
Comments