Search: id:A020137
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%I A020137
%S A020137 9,21,45,63,65,105,117,133,153,231,273,341,481,511,561,585,645,651,861,
%T A020137 949,1001,1105,1281,1365,1387,1417,1541,1649,1661,1729,1785,1905,2047,
%U A020137 2169,2465,2501,2701,2821,3145,3171,3201,3277,3605,3641,4005,4033,4097
%N A020137 Pseudoprimes to base 8.
%C A020137 This sequence is a subsequence of the sequence A122785. In fact the terms 
               are odd composite terms of A122785. Theorem: If both numbers q & 
               2q-1 are primes (q is in the sequence A005382) and n=q*(2q-1) then 
               8^(n-1)==1 (mod n) (n is in the sequence) iff q is of the form 12k+1. 
               2701,18721,49141,104653,226801,665281,721801,... is the related subsequence. 
               This subsequence is also a subsequence of the sequence A122785. - 
               Farideh Firoozbakht (mymontain(AT)yahoo.com), Sep 15 2006
%H A020137 R. J. Mathar, <a href="b020137.txt">Table of n, a(n) for n=1..613</a>
%H A020137 <a href="Sindx_Ps.html#pseudoprimes">Index entries for sequences related 
               to pseudoprimes</a>
%t A020137 Select[Range[4100], ! PrimeQ[ # ] && PowerMod[8, (# - 1), # ] == 1 &] 
               - Farideh Firoozbakht (mymontain(AT)yahoo.com), Sep 15 2006
%Y A020137 Cf. A005382, A122783, A122785.
%Y A020137 Sequence in context: A110680 A163205 A154862 this_sequence A020190 A135187 
               A133762
%Y A020137 Adjacent sequences: A020134 A020135 A020136 this_sequence A020138 A020139 
               A020140
%K A020137 nonn
%O A020137 1,1
%A A020137 David W. Wilson (davidwwilson(AT)comcast.net)

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