A099381 Numbers n such that |Fibonacci(n) - prime(n)| is prime.

2, 3, 6, 8, 9, 12, 15, 24, 33, 48, 225, 525, 948, 1344, 5169, 30600, 32520, 32604, 72396

Offset: 1

Author

Rick L. Shepherd, Nov 16 2004

Keywords

• nonn

Comments

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).

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

Examples

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

Crossrefs

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

Programs

Mathematica

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 *)

PARI

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

Extensions

4 more terms from Jason Earls, Nov 25 2007