Search: id:A005939
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%I A005939 M4612
%S A005939 9,33,91,99,259,451,481,561,657,703,909,1233,1729,2409,2821,2981,3333,
%T A005939 3367,4141,4187,4521,5461,6533,6541,6601,7107,7471,7777,8149,8401,8911,
%U A005939 10001,11111,11169,11649,12403,12801,13833,13981,14701,14817,14911,15211
%N A005939 Pseudoprimes to base 10.
%C A005939 This sequence is a subsequence of A121014 & A121912. In fact the terms 
               are composite terms n of these sequences such that gcd(n,10)=1. Theorem: 
               If both numbers q & 2q-1 are primes(q is in the sequence A005382) 
               and n=q*(2q-1) then 10^(n-1) == 1 (mod n) (n is in the sequence A005939) 
               iff mod(q, 20) is in the set {1, 7, 19}. 91,703,12403,38503,79003,
               188191,269011,... are such terms. - Farideh Firoozbakht (mymontain(AT)yahoo.com), 
               Sep 15 2006
%D A005939 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005939 R. K. Guy, Unsolved Problems in Number Theory, A12.
%H A005939 <a href="Sindx_Ps.html#pseudoprimes">Index entries for sequences related 
               to pseudoprimes</a>
%t A005939 Select[Range[15300], ! PrimeQ[ # ] && PowerMod[10, (# - 1), # ] == 1 
               &] - Farideh Firoozbakht (mymontain(AT)yahoo.com), Sep 15 2006
%Y A005939 Cf. A005382, A121014, A121912.
%Y A005939 Sequence in context: A146171 A146188 A020228 this_sequence A020326 A112888 
               A048479
%Y A005939 Adjacent sequences: A005936 A005937 A005938 this_sequence A005940 A005941 
               A005942
%K A005939 nonn
%O A005939 1,1
%A A005939 N. J. A. Sloane (njas(AT)research.att.com).

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