Search: id:A020138
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%I A020138
%S A020138 4,8,28,52,91,121,205,286,364,511,532,616,671,697,703,946,949,1036,1105,
%T A020138 1288,1387,1541,1729,1891,2465,2501,2665,2701,2806,2821,2926,3052,3281,
%U A020138 3367,3751,4376,4636,4961,5356,5551,6364,6601,6643,7081,7381,7913,8401
%N A020138 Pseudoprimes to base 9.
%C A020138 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
%H A020138 R. J. Mathar, <a href="b020138.txt">Table of n, a(n) for n=1..159</a>
%H A020138 <a href="Sindx_Ps.html#pseudoprimes">Index entries for sequences related 
               to pseudoprimes</a>
%t A020138 Select[Range[8500], ! PrimeQ[ # ] && PowerMod[9, (# - 1), # ] == 1 &] 
               - Farideh Firoozbakht (mymontain(AT)yahoo.com), Sep 15 2006
%Y A020138 Cf. A005382, A122786.
%Y A020138 Sequence in context: A099513 A104042 A117864 this_sequence A090083 A034515 
               A059480
%Y A020138 Adjacent sequences: A020135 A020136 A020137 this_sequence A020139 A020140 
               A020141
%K A020138 nonn
%O A020138 1,1
%A A020138 David W. Wilson (davidwwilson(AT)comcast.net)

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