A099381 - OEIS

%I #8 Dec 15 2017 17:36:47

%S 2,3,6,8,9,12,15,24,33,48,225,525,948,1344,5169,30600,32520,32604,

%T 72396

%N Numbers n such that |Fibonacci(n) - prime(n)| is prime.

%C Fibonacci(n) - prime(n) > 0 for n >= 8. All terms other than 2 and 8 (only two terms producing 2, the only even prime) are divisible by 3 (as Fibonacci(n) is even - and hence |Fibonacci(n) - prime(n)| > 1 and odd - iff n is divisible by 3).

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

%e 9 is a term as Fibonacci(9) - prime(9) = 34 - 23 = 11, a prime.

%t fQ[n_] := PrimeQ[ Fibonacci[n] - Prime[n]]; Do[ If[ fQ[n], Print[n]], {n, 9, 10^4, 3}] (* _Robert G. Wilson v_, Nov 18 2004 *)

%o (PARI) print1(2,",",3,",",6,",",8,","); forstep(n=9,5169,3, if(isprime(fibonacci(n)-prime(n)), print1(n,",")))

%Y Cf. A050180 (Fibonacci(n) + prime(n) is prime).

%K nonn

%O 1,1

%A _Rick L. Shepherd_, Nov 16 2004

%E 4 more terms from _Jason Earls_, Nov 25 2007