Search: id:A005938
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%I A005938 M4168
%S A005938 6,25,325,561,703,817,1105,1825,2101,2353,2465,3277,4525,4825,6697,8321,
%T A005938 10225,10585,10621,11041,11521,12025,13665,14089,16725,16806,18721,19345,
%U A005938 20197,20417,20425,22945,25829,26419,29234,29341,29857,29891,30025,30811
%N A005938 Pseudoprimes to base 7.
%C A005938 According to Karsten Meyer (arbol01(AT)gmx.de), May 16 2006, 6 should 
               be excluded, following the strict definition in Crandall and Pomerance.
%C A005938 Theorem: If both numbers q & 2q-1 are primes(q is in the sequence A005382) 
               and n=q*(2q-1) then 7^(n-1)==1 (mod 7)(n is in the sequence) iff 
               q=2 or mod(q,14) is in the set {1, 5, 13}. 6,703,18721,38503,88831,
               104653,146611,188191,... are such terms. This sequence is a subsequence 
               of A122784. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Sep 14 
               2006
%D A005938 R. Crandall and C. Pomerance, "Prime Numbers - A Computational Perspective", 
               Second Edition, Springer Verlag 2005, ISBN 0-387-25282-7 Page 132 
               (Theorem 3.4.2. and Algorithm 3.4.3)
%D A005938 R. K. Guy, Unsolved Problems in Number Theory, A12.
%D A005938 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005938 R. J. Mathar, <a href="b005938.txt">Table of n, a(n) for n=1..697</a>
%H A005938 J. Bernheiden, <a href="http://www.mathe-schule.de/download/pdf/Primzahl/
               PSP.pdf">Pseudoprimes (Text in German)</a>
%H A005938 F. Richman, <a href="http://www.math.fau.edu/Richman/carm.htm">Primality 
               testing with Fermat's little theorem</a>
%H A005938 <a href="Sindx_Ps.html#pseudoprimes">Index entries for sequences related 
               to pseudoprimes</a>
%t A005938 Select[Range[31000], ! PrimeQ[ # ] && PowerMod[7, (# - 1), # ] == 1 &] 
               - Farideh Firoozbakht (mymontain(AT)yahoo.com), Sep 14 2006
%Y A005938 Cf. A005382, A122784.
%Y A005938 Sequence in context: A042529 A090566 A041064 this_sequence A157025 A036175 
               A154869
%Y A005938 Adjacent sequences: A005935 A005936 A005937 this_sequence A005939 A005940 
               A005941
%K A005938 nonn
%O A005938 1,1
%A A005938 N. J. A. Sloane (njas(AT)research.att.com).

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