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A000047 Number of integers <= 2^n of form x^2 - 2y^2.
(Formerly M0701 N0259)
2
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

D. Shanks and L. P. Schmid, Variations on a theorem of Landau. Part I, Math. Comp., 20 (1966), 551-569.

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

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.

Index entries for sequences related to populations of quadratic forms

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}] [From 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 A006544

Adjacent sequences:  A000044 A000045 A000046 * A000048 A000049 A000050

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Giovanni Resta and Harry J. Smith, Jan 24 2009

STATUS

approved

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Last modified November 22 10:43 EST 2014. Contains 249805 sequences.