Search: id:A005935
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%I A005935 M5362
%S A005935 91,121,286,671,703,949,1105,1541,1729,1891,2465,2665,2701,2821,3281,
%T A005935 3367,3751,4961,5551,6601,7381,8401,8911,10585,11011,12403,14383,15203,
%U A005935 15457,15841,16471,16531,18721,19345,23521,24046,24661,24727,28009,29161
%N A005935 Pseudoprimes to base 3.
%C A005935 Theorem: If q>3 and both numbers q and (2q-1) are primes then n=q*(2q-1) 
               is a pseudoprime to base 3 (i.e. n is in the sequence). So for n>
               2, A005382(n)*(2*A005382(n)-1) is in the sequence (see Comments lines 
               for the sequence A122780). 91,703,1891,2701,12403,18721,38503,49141... 
               are such terms. This sequence is a subsequence of A122780. - Farideh 
               Firoozbakht (mymontain(AT)yahoo.com), Sep 13 2006
%D A005935 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 91, p. 33, Ellipses, 
               Paris 2008.
%D A005935 R. K. Guy, Unsolved Problems in Number Theory, A12.
%D A005935 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005935 R. J. Mathar, <a href="b005935.txt">Table of n, a(n) for n=1..798</a>
%H A005935 J. Bernheiden, <a href="http://www.mathe-schule.de/download/pdf/Primzahl/
               PSP.pdf">Pseudoprimes (Text in German)</a>
%H A005935 F. Richman, <a href="http://www.math.fau.edu/Richman/carm.htm">Primality 
               testing with Fermat's little theorem</a>
%H A005935 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               FermatPseudoprime.html">Fermat Pseudoprime</a>
%H A005935 <a href="Sindx_Ps.html#pseudoprimes">Index entries for sequences related 
               to pseudoprimes</a>
%Y A005935 Cf. A005382, A122780.
%Y A005935 Sequence in context: A140389 A157345 A092125 this_sequence A020307 A020235 
               A046427
%Y A005935 Adjacent sequences: A005932 A005933 A005934 this_sequence A005936 A005937 
               A005938
%K A005935 nonn
%O A005935 1,1
%A A005935 N. J. A. Sloane (njas(AT)research.att.com).
%E A005935 More terms from David W. Wilson Aug 15 1996.

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