Search: id:A000047
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%I A000047 M0701 N0259
%S A000047 1,2,3,5,8,15,26,48,87,161,299,563,1066,2030,3885,7464,14384,27779,
%T A000047 53782,104359,202838,394860,769777,1502603,2936519,5744932,11249805,
%U A000047 22048769,43248623,84894767,166758141,327770275,644627310,1268491353,2497412741
%N A000047 Number of integers <= 2^n of form x^2 - 2y^2.
%D A000047 D. Shanks and L. P. Schmid, Variations on a theorem of Landau. Part I, 
               Math. Comp., 20 (1966), 551-569.
%D A000047 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000047 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000047 Ray Chandler, <a href="b000047.txt">Table of n, a(n) for n=0..35</a>
%H A000047 D. Borwein, J. M. Borwein, P. B. Borwein, R. Girgensohn, <a href="http:/
               /www.jstor.org/stable/2975213">Giuga's Conjecture on Primality</a>
               , Am. Math. Monthly 103 (1) (1996), 40-50. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jan 20 2009]
%H A000047 <a href="Sindx_Qua.html#quadpop">Index entries for sequences related 
               to populations of quadratic forms</a>
%t A000047 cnt=0; n=0; Table[n++; While[{p,e}=Transpose[FactorInteger[n]]; If[Select[p^e, 
               MemberQ[{3,5}, Mod[ #,8]] &] == {}, cnt++ ]; n<2^k, n++ ]; cnt, {k,
               0,20}] [From T. D. Noe (noe(AT)sspectra.com), Jan 19 2009]
%o A000047 (PARI) A000047(n)={ local(f,c=0); for(m=1,2^n, for(i=1,#f=factor(m)~, 
               abs(f[1,i]%8-4)==1 | next; f[2,i]%2 & next(2));c++);c} /* cf. comment 
               in A035251: m=3 or 5 mod 8 */ [From M. F. Hasler (MHasler(AT)univ-ag.fr), 
               Jan 19 2009]
%Y A000047 Cf. A035251.
%Y A000047 Sequence in context: A006982 A054539 A026702 this_sequence A101172 A006544 
               A110536
%Y A000047 Adjacent sequences: A000044 A000045 A000046 this_sequence A000048 A000049 
               A000050
%K A000047 nonn
%O A000047 0,2
%A A000047 N. J. A. Sloane (njas(AT)research.att.com).
%E A000047 More terms from Giovanni Resta (g.resta(AT)iit.cnr.it) and Harry J. Smith 
               (hjsmithh(AT)sbcglobal.net), Jan 24 2009

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