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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

Seth A. Troisi, Table of n, a(n) for n = 0..50 (terms 0..35 from Ray Chandler, 36..37 from Pontus von Brömssen)

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.

Index entries for sequences related to populations of quadratic forms

Seth A. Troisi, C++ and Python programs

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

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 October 1 16:19 EDT 2022. Contains 357149 sequences. (Running on oeis4.)