A078735 - OEIS

%I #10 Apr 26 2023 10:04:42

%S 0,3,5,9,13,18,37,384,569,2760,3293

%N a(0) = 0, a(1) = 3; a(n+1) = the smallest x such that Fibonacci(x)-Fibonacci(a(n)) is both prime and greater than Fibonacci(a(n))-Fibonacci(a(n-1)).

%C Some of the larger entries may only correspond to probable primes.

%F A078727(n) = Fibonacci(a(n))-Fibonacci(a(n-1)).

%t a[0] = 0; a[1] = 3; a[n_] := a[n] = Block[{d = Fibonacci[a[n - 1]] - Fibonacci[a[n - 2]], f = Fibonacci[a[n - 1]], k = a[n - 1] + 1}, While[Fibonacci[k] - f <= d || !PrimeQ[Fibonacci[k] - f], k++ ]; k]; Do[ Print[ a[n]], {n, 0, 10}] (* _Robert G. Wilson v_ *)

%Y A more compact version of A078727.

%Y Cf. A000045.

%K nonn

%O 0,2

%A _Jack Brennen_, Dec 20 2002

%E a(10) from _Robert G. Wilson v_, Nov 30 2005