A050937 Nonprime Fibonacci numbers with a prime index.

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

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

Cf. A038672 (indices).

Sequence in context: A045728 A048593 A358555 * A135953 A290846 A236805

Adjacent sequences: A050934 A050935 A050936 * A050938 A050939 A050940

Keyword

nonn,easy

Author

Jud McCranie, Jan 01 2000

Status

approved