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A001602
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Fibonacci entry points: a(n) = smallest m > 0 such that the n-th prime divides Fibonacci(m).
(Formerly M2310 N0912)
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19
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3, 4, 5, 8, 10, 7, 9, 18, 24, 14, 30, 19, 20, 44, 16, 27, 58, 15, 68, 70, 37, 78, 84, 11, 49, 50, 104, 36, 27, 19, 128, 130, 69, 46, 37, 50, 79, 164, 168, 87, 178, 90, 190, 97, 99, 22, 42, 224, 228, 114, 13, 238, 120, 250, 129, 88, 67, 270, 139, 28, 284, 147, 44, 310
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| "[a(n)] is called by Lucas the rank of apparition of p and we know it is a divisor of, or equal to p-1 or p+1" - Vajda, p. 84. [Note that a(5)=5. This is the only exception. - Chris Caldwell, Nov 03 2008]
Every number except 1, 2, 6 and 12 eventually occurs in this sequence. The number of times n occurs is A086597(n), the number of primitive prime factors of Fibonacci(n). - T. D. Noe, Jun 13 2008
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REFERENCES
| A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 25.
D. E. Daykin and L. A. G. Dresel, Fibonacci Quarterly, vol 7 (1969), pages 23 - 30 and 82.
Ramon Glez-Regueral, An entry-point algorithm for high-speed factorization, Thirteenth Internat. Conf. Fibonacci Numbers Applications, Patras, Greece, 2008.
D. Jarden, Recurring Sequences. Riveon Lematematika, Jerusalem, 1966.
D. Lind et al., Tables of Fibonacci entry points, part 2, reviewed in Math. Comp., 20 (1966), 618-619.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. Vajda, Fibonacci and Lucas numbers and the Golden Section, Ellis Horwood Ltd., Chichester, 1989.
M. Wunderlich, Tables of Fibonacci entry points, reviewed in Math. Comp., 20 (1966), 618-619.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
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FORMULA
| a(n) <= prime(n)^2. [Charles R Greathouse IV, Jul 31 2011]
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EXAMPLE
| The 5th prime is 11 and 11 first divides Fib(10)=55, so a(5) = 10.
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CROSSREFS
| Cf. A051694, A001177.
Sequence in context: A050590 A066906 A125884 * A087012 A047366 A184776
Adjacent sequences: A001599 A001600 A001601 * A001603 A001604 A001605
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu)
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