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A005939
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Pseudoprimes to base 10.
(Formerly M4612)
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2
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9, 33, 91, 99, 259, 451, 481, 561, 657, 703, 909, 1233, 1729, 2409, 2821, 2981, 3333, 3367, 4141, 4187, 4521, 5461, 6533, 6541, 6601, 7107, 7471, 7777, 8149, 8401, 8911, 10001, 11111, 11169, 11649, 12403, 12801, 13833, 13981, 14701, 14817, 14911, 15211
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| This sequence is a subsequence of A121014 & A121912. In fact the terms are composite terms n of these sequences such that gcd(n,10)=1. Theorem: If both numbers q & 2q-1 are primes(q is in the sequence A005382) and n=q*(2q-1) then 10^(n-1) == 1 (mod n) (n is in the sequence A005939) iff mod(q, 20) is in the set {1, 7, 19}. 91,703,12403,38503,79003,188191,269011,... are such terms. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Sep 15 2006
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REFERENCES
| R. K. Guy, Unsolved Problems in Number Theory, A12.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Index entries for sequences related to pseudoprimes
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MATHEMATICA
| Select[Range[15300], ! PrimeQ[ # ] && PowerMod[10, (# - 1), # ] == 1 &] - Farideh Firoozbakht (mymontain(AT)yahoo.com), Sep 15 2006
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CROSSREFS
| Cf. A005382, A121014, A121912.
Sequence in context: A146171 A146188 A020228 * A020326 A201024 A112888
Adjacent sequences: A005936 A005937 A005938 * A005940 A005941 A005942
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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