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%I M0701 N0259 #48 Dec 19 2022 10:17:26
%S 1,2,3,5,8,15,26,48,87,161,299,563,1066,2030,3885,7464,14384,27779,
%T 53782,104359,202838,394860,769777,1502603,2936519,5744932,11249805,
%U 22048769,43248623,84894767,166758141,327770275,644627310,1268491353,2497412741
%N Number of integers <= 2^n of form x^2 - 2y^2.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Seth A. Troisi, <a href="/A000047/b000047.txt">Table of n, a(n) for n = 0..50</a> (terms 0..35 from Ray Chandler, 36..37 from Pontus von Brömssen)
%H 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.
%H D. Shanks and L. P. Schmid, <a href="http://dx.doi.org/10.1090/S0025-5718-1966-0210678-1">Variations on a theorem of Landau. Part I</a>, Math. Comp., 20 (1966), 551-569.
%H <a href="/index/Qua#quadpop">Index entries for sequences related to populations of quadratic forms</a>
%H Seth A. Troisi, <a href="https://github.com/sethtroisi/OEIS/tree/main/A000047">C++ and Python programs</a>
%e There are 5 integers <= 2^3 of form x^2 - 2y^2. The five (x,y) pairs (1,0), (2,1), (2,0), (3,1), (4,2) give respectively: 1, 2, 4, 7, 8. So a(3) = 5. - _Bernard Schott_, Feb 10 2019
%t 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}] (* _T. D. Noe_, Jan 19 2009 *)
%o (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} \\ See comment in A035251: m=3 or 5 mod 8; _M. F. Hasler_, Jan 19 2009
%Y Cf. A035251.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Giovanni Resta_ and _Harry J. Smith_, Jan 24 2009
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