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Search: id:A020138
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| A020138 |
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Pseudoprimes to base 9. |
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+0
3
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| 4, 8, 28, 52, 91, 121, 205, 286, 364, 511, 532, 616, 671, 697, 703, 946, 949, 1036, 1105, 1288, 1387, 1541, 1729, 1891, 2465, 2501, 2665, 2701, 2806, 2821, 2926, 3052, 3281, 3367, 3751, 4376, 4636, 4961, 5356, 5551, 6364, 6601, 6643, 7081, 7381, 7913, 8401
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This sequence is a subsequence of A122786. In fact the terms are composite terms n of A122786 such that gcd(n,3)=1. Theorem: If both numbers q & 2q-1 are primes greater than 3 and n=q*(2q-1) then 9^(n-1)==1 (mod n) (n is in the sequence). So for n>2 A005382(n)* (2*A005382(n)-1) is in the sequence; 91,703,1891,2701,12403,18721,... is the related subsequence. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Sep 15 2006
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LINKS
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R. J. Mathar, Table of n, a(n) for n=1..159
Index entries for sequences related to pseudoprimes
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MATHEMATICA
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Select[Range[8500], ! PrimeQ[ # ] && PowerMod[9, (# - 1), # ] == 1 &] - Farideh Firoozbakht (mymontain(AT)yahoo.com), Sep 15 2006
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CROSSREFS
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Cf. A005382, A122786.
Sequence in context: A099513 A104042 A117864 this_sequence A090083 A034515 A059480
Adjacent sequences: A020135 A020136 A020137 this_sequence A020139 A020140 A020141
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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