OFFSET
1,3
COMMENTS
This set is conjectured to have zero density. The only even values are the numbers of the form 2n^2. See the paper by Cooper, Eichhorn and O'Bryant for more details. - Franklin T. Adams-Watters, May 16 2006
In a note on arXiv, "Disquisitiones Arithmeticae and online sequence A108345", I show that the upper density is at most 1/16. Furthermore computer evidence presented there suggests that the density is not 0, but 1/32. [From Paul Monsky (monsky(AT)brandeis.edu), Sep 24 2010]
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
J. N. Cooper, D. Eichhorn and K. O'Bryant, Reciprocals of binary power series
Paul Monsky, Disquisitiones Arithmeticae and online sequence A108345 [From Paul Monsky (monsky(AT)brandeis.edu), Sep 24 2010]
FORMULA
The terms are the exponents in the expansion of 1/(Sum_{ n >= 0 } x^(n^2)) read mod 2. - N. J. A. Sloane, Dec 12 2007
MAPLE
N:= 500: # to get all terms <= N
S:= series(1/add(x^(n^2), n=0..floor(sqrt(N))), x, N+1) mod 2:
select(t -> coeff(S, x, t)=1, [$0..N]); # Robert Israel, Jun 01 2016
MATHEMATICA
Exponent[#, x]& /@ List @@ (Normal[2/(1+EllipticTheta[3, 0, x])+ O[x]^200] /. n_ x^k_ -> Mod[n, 2] x^k) (* Jean-François Alcover, Sep 17 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ralf Stephan, Jul 01 2005
EXTENSIONS
More terms from Franklin T. Adams-Watters, May 16 2006
Changed comment "this set has zero density" to "this set is conjectured to have zero density". - Kevin O'Bryant, Jul 09 2010
STATUS
approved