A050937 Nonprime Fibonacci numbers with a prime index.

1, 4181, 1346269, 24157817, 165580141, 53316291173, 956722026041, 2504730781961, 44945570212853, 308061521170129, 806515533049393, 14472334024676221, 1779979416004714189, 83621143489848422977

Offset: 1

Author

Jud McCranie, Jan 01 2000

Keywords

• nonn
• easy

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.

Examples

			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.
		

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

Crossrefs

Cf. A038672 (indices).

Programs

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 *)

PARI

f(n) = forprime(x=2,n,p=fibonacci(x);if(!isprime(p),print1(p","))) \\ Cino Hilliard, Feb 11 2004