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 A000047 Number of integers <= 2^n of form x^2 - 2y^2. (Formerly M0701 N0259) 3
 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; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Pontus von Brömssen, Table of n, a(n) for n = 0..37 (terms 0..35 from Ray Chandler) D. Borwein, J. M. Borwein, P. B. Borwein, R. Girgensohn, Giuga's Conjecture on Primality, Am. Math. Monthly 103 (1) (1996), 40-50. D. Shanks and L. P. Schmid, Variations on a theorem of Landau. Part I, Math. Comp., 20 (1966), 551-569. EXAMPLE 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 MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A035251. Sequence in context: A006982 A054539 A026702 * A101172 A192677 A307909 Adjacent sequences:  A000044 A000045 A000046 * A000048 A000049 A000050 KEYWORD nonn AUTHOR EXTENSIONS More terms from Giovanni Resta and Harry J. Smith, Jan 24 2009 STATUS approved

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Last modified December 7 13:08 EST 2021. Contains 349581 sequences. (Running on oeis4.)