Search: id:A077816
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%I A077816
%S A077816 1093,3279,3511,7651,10533,14209,17555,22953,31599,42627,45643,52665,
%T A077816 68859,94797,99463,127881,136929,157995,228215,298389,410787,473985,
%U A077816 684645,895167,1232361,2053935,2685501,3697083,3837523,6161805,11512569
%N A077816 Wieferich numbers: n such that 2^phi(n) == 1 modulo n^2.
%C A077816 A077815(a(n))=1;
%C A077816 The only known primes are a(1)=A001220(1)=1093 and a(3)=A001220(2)=3511, 
               the Wieferich primes.
%D A077816 R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, 
               Springer, NY, 2001; see p. 28.
%H A077816 RICHARD CRANDALL, KARL DILCHER and CARL POMERANCE, <a href="http://www.math.dartmouth.edu/
               ~carlp/PDF/paper111.pdf">A SEARCH FOR WIEFERICH AND WILSON PRIMES</
               a>, Mathematics of Computation, Volume 66, 1997.
%e A077816 A077815(3279) = 2^phi(3279) mod 3279*3279 = 2^phi(3*1093) mod 10751841 
               = 2^(3279*(1-1/3)*(1-1/1093)) mod 10751841 = 2^2184 mod 10751841 
               = 1, therefore 3279 is a term
%Y A077816 Cf. A001220.
%Y A077816 Sequence in context: A138698 A023698 A038469 this_sequence A001220 A115192 
               A091674
%Y A077816 Adjacent sequences: A077813 A077814 A077815 this_sequence A077817 A077818 
               A077819
%K A077816 nonn
%O A077816 1,1
%A A077816 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 17 2002
%E A077816 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 05 2005
%E A077816 More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Jun 18 2005

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