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Search: id:A072381
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| A072381 |
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Numbers n such that Fibonacci(n) is a semiprime. |
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+0
4
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| 8, 9, 10, 14, 19, 22, 26, 31, 34, 41, 53, 59, 61, 71, 73, 79, 89, 94, 101, 107, 109, 113, 121, 127, 151, 167, 173, 191, 193, 199, 227, 251, 271, 277, 293, 331, 353, 397, 401, 467, 587, 599, 601, 613, 631, 653, 743, 991
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OFFSET
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1,1
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COMMENT
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Note that there are two cases: (1) n is 2p, in which case the semiprime is Fibonacci(p)*Lucas(p) for some prime p, or (2) n is a power of a prime p^k for k>0. In the first case, the primes p are in sequence A080327. In the second case, it appears that k=1 except for n = 8, 9, and 121. - T. D. Noe (noe(AT)sspectra.com), Sep 23 2005
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REFERENCES
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Y. Bugeaud, F. Luca, M. Mignotte, and S. Siksek, On Fibonacci numbers with few prime divisors, Proc. Japan Acad., 81, Ser. A (2005), pp. 17-20.
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LINKS
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R. Knott, Fibonacci numbers
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EXAMPLE
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a(4)=14, so 14th Fibonacci number i.e. 377 is a semiprime (377=13*29).
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MATHEMATICA
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Select[Range[200], Plus@@Last/@FactorInteger[Fibonacci[ # ]] == 2&] (Noe)
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CROSSREFS
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Cf. A053409.
Cf. A085726 (n such that n-th Lucas number is a semiprime).
Sequence in context: A054011 A114842 A067683 this_sequence A046415 A091417 A069237
Adjacent sequences: A072378 A072379 A072380 this_sequence A072382 A072383 A072384
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KEYWORD
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nonn
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AUTHOR
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Shyam Sunder Gupta (guptass(AT)rediffmail.com), Jul 20 2002
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EXTENSIONS
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More terms from Don Reble (djr(AT)nk.ca), Jul 31 2002
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