A038672 -id:A038672 - cp's OEIS frontend

A050937 Nonprime Fibonacci numbers with a prime index.

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

Offset: 1

Jud McCranie, Jan 01 2000

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.

			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.

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

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

Cf. A038672 (indices).

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

Select[Table[Fibonacci[Prime[n]], {n, 25}], Not[PrimeQ[#]] &] (* Alonso del Arte, Nov 22 2010 *)

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

A090819 Primes p such that the p-th Fibonacci number is nonprime.

Original entry on oeis.org

2, 19, 31, 37, 41, 53, 59, 61, 67, 71, 73, 79, 89, 97, 101, 103, 107, 109, 113, 127, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349

Offset: 1

Cino Hilliard, Feb 11 2004

Is it true that a(n) ~ n log n? - Charles R Greathouse IV, Aug 15 2015

			Fibonacci(37) = 24157817 = 73*149*2221. [corrected by _Bobby Jacobs_, Sep 25 2017]

Cf. A000045, A001605, A134787.

Essentially the same as A038672.

Select[Prime[Range[62]], ! PrimeQ[Fibonacci[#]] &] (* Jayanta Basu, Jul 10 2013 *)

f(n) = forprime(x=2,n,p=fibonacci(x);if(!isprime(p),print1(x",")))

a(n) = prime(A134787(n)). - Amiram Eldar, Oct 25 2024

Definition corrected by Don Reble, Sep 04 2008

A238082 Composites occurring as divisors of Fibonacci(p) with p prime.

Original entry on oeis.org

4181, 10877, 75077, 162133, 330929, 1256293, 1346269, 2662277, 3636121, 4226777, 9401893, 13455077, 14787181, 16485493, 21692189, 24157817, 24493061, 25532501, 29604893, 31432381, 39247393, 73780877, 75245777, 77337941, 120485381, 124477513, 127835341, 132162581, 143221993, 143548501

Offset: 1

Hans Havermann, Antti Karttunen and David W. Wilson, Feb 02 2014

nonn

The first two non-semiprimes are a(16) = 73 * 149 * 2221 and a(254) = 1453 * 2909 * 10177.

David Wilson and Hans Havermann, Table of n, a(n) for n = 1..338 [David Wilson to 148, Hans Havermann to 338]
Hans Havermann, A238082 factored
Hans Havermann, Composite Prime-Index Fibonacci Numbers Factored
Antti Karttunen, More composite terms for A233281

The sequence gives composite values of A233281.

Cf. A038672, A092395, A135952.

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A050937 Nonprime Fibonacci numbers with a prime index.

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A090819 Primes p such that the p-th Fibonacci number is nonprime.

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A238082 Composites occurring as divisors of Fibonacci(p) with p prime.

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