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A006945
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Smallest odd number that requires n Miller-Rabin primality tests.
(Formerly M4673)
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2
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9, 2047, 1373653, 25326001, 3215031751, 2152302898747, 3474749660383, 341550071728321, 341550071728321, 3825123056546413051, 3825123056546413051, 3825123056546413051
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OFFSET
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1,1
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COMMENTS
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The tests are performed on sequential prime numbers starting with 2. Note that some terms are repeated.
Same as A014233 except for the first term.
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REFERENCES
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R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 157.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=1..12.
Joerg Arndt, Fxtbook
G. Jaeschke, On strong pseudoprimes to several bases, Math. Comp., 61 (1993), 915-926.
Yupeng Jiang, Yingpu Deng, Strong pseudoprimes to the first 9 prime bases, arXiv:1207.0063v1 [math.NT], June 30, 2012.
C. Pomerance, J. L. Selfridge and S. S. Wagstaff, Jr., The pseudoprimes to 25.10^9, Mathematics of Computation 35 (1980), pp. 1003-1026.
S. Wagon, Primality testing, Math. Intellig., 8 (No. 3, 1986), 58-61.
Zhenxiang Zhang and Min Tang, Finding strong pseudoprimes to several bases. II, Mathematics of Computation 72 (2003), pp. 2085-2097.
Eric Bach, Explicit bounds for primality testing and related problems, Mathematics of Computation 55 (1990), pp. 355-380.
Index entries for sequences related to pseudoprimes
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FORMULA
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Bach shows that, on the ERH, a(n) >> exp(sqrt(1/2 * x log x)). [Charles R Greathouse IV, May 17, 2011]
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CROSSREFS
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Cf. A089105, A089825.
Sequence in context: A024125 A039917 A162140 * A089825 A173281 A004820
Adjacent sequences: A006942 A006943 A006944 * A006946 A006947 A006948
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KEYWORD
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nonn,hard,more,changed
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Extended and description corrected by Jud McCranie Feb 15 1997.
a(10)-a(12) from Charles R Greathouse IV, Aug 14 2010
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STATUS
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approved
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