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Search: id:A000047
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| A000047 |
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Number of integers <= 2^n of form x^2 - 2y^2.
(Formerly M0701 N0259)
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+0
2
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| 1, 2, 3, 5, 8, 15, 26, 48, 87, 161, 299, 563, 1066, 2030, 3885, 7464, 14384, 27779, 53782, 104359, 202838, 394860, 769777, 1502603, 2936519, 5744932, 11249805, 22048769, 43248623, 84894767, 166758141, 327770275, 644627310, 1268491353, 2497412741
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
D. Shanks and L. P. Schmid, Variations on a theorem of Landau. Part I, Math. Comp., 20 (1966), 551-569.
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LINKS
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Ray Chandler, Table of n, a(n) for n=0..35
D. Borwein, J. M. Borwein, P. B. Borwein, R. Girgensohn, Giuga's Conjecture on Primality, Am. Math. Monthly 103 (1) (1996), 40-50. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 20 2009]
Index entries for sequences related to populations of quadratic forms
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MATHEMATICA
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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]
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PROGRAM
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(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]
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CROSSREFS
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Cf. A035251.
Adjacent sequences: A000044 A000045 A000046 this_sequence A000048 A000049 A000050
Sequence in context: A006982 A054539 A026702 this_sequence A101172 A006544 A110536
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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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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