Search: id:A020136
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%I A020136
%S A020136 15,85,91,341,435,451,561,645,703,1105,1247,1271,1387,1581,1695,1729,
%T A020136 1891,1905,2047,2071,2465,2701,2821,3133,3277,3367,3683,4033,4369,4371,
%U A020136 4681,4795,4859,5461,5551,6601,6643,7957,8321,8481,8695,8911,9061,9131
%N A020136 Pseudoprimes to base 4.
%C A020136 Primes q and 2q-1 are a Cunningham chain of the second kind. [From Walter 
               Nissen (nissen(AT)gtcinternet.com), Sep 07 2009]
%H A020136 <a href="Sindx_Ps.html#pseudoprimes">Index entries for sequences related 
               to pseudoprimes</a>
%H A020136 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               FermatPseudoprime.html">Fermat Pseudoprime</a>
%H A020136 Chris Caldwell, <a href="http://primes.utm.edu/glossary/xpage/CunninghamChain.html"> 
               Cunningham chain</a> [From Walter Nissen (nissen(AT)gtcinternet.com), 
               Sep 07 2009]
%H A020136 Chris Caldwell, et al., <a href="http://primes.utm.edu/top20/page.php?id=20"> 
               Top Twenty Cunningham Chains (2nd kind)</a> [From Walter Nissen (nissen(AT)gtcinternet.com), 
               Sep 07 2009]
%F A020136 Theorem: If q and 2q-1 are odd primes then n=q*(2q-1) is in the sequence. 
               So for n>1 A005382(n)*(2*A005382(n)-1) is in the sequence - 15, 91, 
               703, 1891, 2701, 12403, 18721, ... is the related subsequence. - 
               Farideh Firoozbakht (mymontain(AT)yahoo.com), Sep 12 2006
%t A020136 Select[Range[9200], ! PrimeQ[ # ] && Mod[4^(# - 1), # ] == 1 &] - Farideh 
               Firoozbakht (mymontain(AT)yahoo.com), Sep 12 2006
%Y A020136 Cf. A005382, A122781.
%Y A020136 Sequence in context: A065103 A108674 A050405 this_sequence A067401 A160599 
               A091286
%Y A020136 Adjacent sequences: A020133 A020134 A020135 this_sequence A020137 A020138 
               A020139
%K A020136 nonn
%O A020136 1,1
%A A020136 David W. Wilson (davidwwilson(AT)comcast.net)

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