A050937 - OEIS

%I #28 Jan 05 2025 19:51:36

%S 1,4181,1346269,24157817,165580141,53316291173,956722026041,

%T 2504730781961,44945570212853,308061521170129,806515533049393,

%U 14472334024676221,1779979416004714189,83621143489848422977

%N Nonprime Fibonacci numbers with a prime index.

%C 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.

%D David Wells, The Penguin Dictionary of Curious and Interesting Numbers, entry 4181.

%H Amiram Eldar, <a href="/A050937/b050937.txt">Table of n, a(n) for n = 1..620</a>

%H Vladimir Drobot, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/38-1/drobot.pdf">On primes in the Fibonacci sequence</a>, Fib. Quart. 38 (1) (2000) 71

%e Fibonacci(2) = 1 is not prime, but its index 2 is prime.

%e Fibonacci(19) = 4181 is a composite Fibonacci number, but its index 19 is prime.

%p for n from 1 to 200 do if isprime(n) and (not isprime( fibonacci(n))) then print( fibonacci(n)): fi: od:

%t Select[Table[Fibonacci[Prime[n]], {n, 25}], Not[PrimeQ[#]] &] (* _Alonso del Arte_, Nov 22 2010 *)

%o (PARI) f(n) = forprime(x=2,n,p=fibonacci(x);if(!isprime(p),print1(p","))) \\ _Cino Hilliard_, Feb 11 2004

%Y Cf. A038672 (indices).

%K nonn,easy

%O 1,2

%A _Jud McCranie_, Jan 01 2000