A133320 Numbers k such that both A124296(k) = 5*F(k)^2 - 5*F(k) + 1 and A124297(k) = 5*F(k)^2 + 5*F(k) + 1 are prime, where F(k) = Fibonacci(k).

3, 4, 5, 10, 40

Offset: 1

Author

Alexander Adamchuk, Oct 18 2007

Keywords

• more
• nonn

Crossrefs

Cf. A124297 (5*F(n)^2 + 5*F(n) + 1, where F(n) = Fibonacci(n)).

Cf. A124296 (5*F(n)^2 - 5*F(n) + 1, where F(n) = Fibonacci(n)).

Cf. A000032, A000045, A121171, A001946.

Programs

Mathematica

Do[ F=Fibonacci[n]; f=5*F^2-5*F+1; g=5*F^2+5*F+1; If[ PrimeQ[f], If[ PrimeQ[g], Print[ {n,f,g} ] ] ], {n,1,1000} ]