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A050937
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Composite Fibonacci numbers with a prime index.
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21
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1, 4181, 1346269, 24157817, 165580141, 53316291173, 956722026041, 2504730781961, 44945570212853, 308061521170129, 806515533049393, 14472334024676221, 1779979416004714189, 83621143489848422977
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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.
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REFERENCES
| David Wells, The Penguin Dictionary of Curious and Interesting Numbers, entry 4181.
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LINKS
| Vladimir Drobot, On primes in the Fibonacci sequence, Fib. Quart. 38 (1) (2000) 71
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EXAMPLE
| Fibonacci(19) = 4181 is a composite Fibonacci number, but its index 19 is prime.
Fibonacci(2) = 1 is a nonprime with a prime index, so is Fibonacci(19) = 4181 = 37*113.
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MAPLE
| for n from 1 to 200 do if isprime(n) and (not isprime( fibonacci(n))) then print( fibonacci(n)): fi: od:
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MATHEMATICA
| Select[Table[Fibonacci[Prime[n]], {n, 25}], Not[PrimeQ[#]]&] (* From Alonso del Arte, alonso.delarte(AT)gmail.com, Nov 22 2010 *)
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PROG
| (PARI) f(n) = forprime(x=2, n, p=fibonacci(x); if(!isprime(p), print1(p", ")))- Cino Hilliard (hillcino368(AT)gmail.com), Feb 11 2004
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CROSSREFS
| A038672 gives the indices.
Sequence in context: A072322 A045728 A048593 * A135953 A202530 A152511
Adjacent sequences: A050934 A050935 A050936 * A050938 A050939 A050940
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KEYWORD
| nonn
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AUTHOR
| Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu), Jan 01 2000
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