OFFSET
1,2
COMMENTS
A Fibonacci number with a composite index is divisible by the Fibonacci numbers indexed by the divisors of the index (e.g., F(12) is divisible by F(3), F(4), F(6)), which would suggest that Fibonacci numbers indexed by primes are also themselves primes. This sequence clearly shows that not to be the case.
REFERENCES
David Wells, The Penguin Dictionary of Curious and Interesting Numbers, entry 4181.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..620
Vladimir Drobot, On primes in the Fibonacci sequence, Fib. Quart. 38 (1) (2000) 71
EXAMPLE
Fibonacci(2) = 1 is not prime, but its index 2 is prime.
Fibonacci(19) = 4181 is a composite Fibonacci number, but its index 19 is prime.
MAPLE
for n from 1 to 200 do if isprime(n) and (not isprime( fibonacci(n))) then print( fibonacci(n)): fi: od:
MATHEMATICA
Select[Table[Fibonacci[Prime[n]], {n, 25}], Not[PrimeQ[#]] &] (* Alonso del Arte, Nov 22 2010 *)
PROG
(PARI) f(n) = forprime(x=2, n, p=fibonacci(x); if(!isprime(p), print1(p", "))) \\ Cino Hilliard, Feb 11 2004
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jud McCranie, Jan 01 2000
STATUS
approved