This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A050937 #28 Jan 05 2025 19:51:36
%S A050937 1,4181,1346269,24157817,165580141,53316291173,956722026041,
%T A050937 2504730781961,44945570212853,308061521170129,806515533049393,
%U A050937 14472334024676221,1779979416004714189,83621143489848422977
%N A050937 Nonprime Fibonacci numbers with a prime index.
%C A050937 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 A050937 David Wells, The Penguin Dictionary of Curious and Interesting Numbers, entry 4181.
%H A050937 Amiram Eldar, <a href="/A050937/b050937.txt">Table of n, a(n) for n = 1..620</a>
%H A050937 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 A050937 Fibonacci(2) = 1 is not prime, but its index 2 is prime.
%e A050937 Fibonacci(19) = 4181 is a composite Fibonacci number, but its index 19 is prime.
%p A050937 for n from 1 to 200 do if isprime(n) and (not isprime( fibonacci(n))) then print( fibonacci(n)): fi: od:
%t A050937 Select[Table[Fibonacci[Prime[n]], {n, 25}], Not[PrimeQ[#]] &] (* _Alonso del Arte_, Nov 22 2010 *)
%o A050937 (PARI) f(n) = forprime(x=2,n,p=fibonacci(x);if(!isprime(p),print1(p","))) \\ _Cino Hilliard_, Feb 11 2004
%Y A050937 Cf. A038672 (indices).
%K A050937 nonn,easy
%O A050937 1,2
%A A050937 _Jud McCranie_, Jan 01 2000