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Search: id:A005935
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| A005935 |
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Pseudoprimes to base 3.
(Formerly M5362)
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+0
4
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| 91, 121, 286, 671, 703, 949, 1105, 1541, 1729, 1891, 2465, 2665, 2701, 2821, 3281, 3367, 3751, 4961, 5551, 6601, 7381, 8401, 8911, 10585, 11011, 12403, 14383, 15203, 15457, 15841, 16471, 16531, 18721, 19345, 23521, 24046, 24661, 24727, 28009, 29161
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Theorem: If q>3 and both numbers q and (2q-1) are primes then n=q*(2q-1) is a pseudoprime to base 3 (i.e. n is in the sequence). So for n>2, A005382(n)*(2*A005382(n)-1) is in the sequence (see Comments lines for the sequence A122780). 91,703,1891,2701,12403,18721,38503,49141... are such terms. This sequence is a subsequence of A122780. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Sep 13 2006
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, A12.
J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 91, p. 33, Ellipses, Paris 2008.
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LINKS
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R. J. Mathar, Table of n, a(n) for n=1..98
F. Richman, Primality testing with Fermat's little theorem
Eric Weisstein's World of Mathematics, Fermat Pseudoprime
Index entries for sequences related to pseudoprimes
J. Bernheiden, Pseudoprimes (Text in German)
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CROSSREFS
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Cf. A005382, A122780.
Adjacent sequences: A005932 A005933 A005934 this_sequence A005936 A005937 A005938
Sequence in context: A020223 A140389 A092125 this_sequence A020307 A020235 A046427
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KEYWORD
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nonn
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AUTHOR
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njas
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EXTENSIONS
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More terms from David W. Wilson Aug 15 1996.
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