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

1,1

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.

Links

Table of n, a(n) for n=1..19.

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A287659 A047244 A111215 * A289943 A089437 A146768

Adjacent sequences: A099378 A099379 A099380 * A099382 A099383 A099384

Keyword

nonn

Author

Rick L. Shepherd, Nov 16 2004

Extensions

4 more terms from Jason Earls, Nov 25 2007

Status

approved