OFFSET
1,2
COMMENTS
The rational partial products are r(n) = a(n)/A191999(n), n >= 1.
The limit r(n), n->infinity, approximately 1.3728134 is the constant C(f) appearing in the Hardy-Littlewood conjecture (also called Bateman-Horn conjecture) for the integer polynomial f=x^2+1. See the Conrad reference Example 2, p. 134, also for the original references.
Note that the nontrivial Dirichlet character modulo 4, called Chi_2(4;n) = A056594(n-1), n >= 1, appears as Chi_4(n) in this reference. The constant 0.6864067 given there is C(f)/2 (the degree of the function f has been divided).
REFERENCES
Keith Conrad, Hardy-Littlewood constants, pp. 133-154 in: Mathematical properties of sequences and other combinatorial structures, edts. Jong-Seon No et al., Kluwer, Boston/Dordrecht/London, 2003.
LINKS
Wolfdieter Lang, Rationals and limit.
FORMULA
EXAMPLE
The rationals r(n) are: 1, 3/2, 9/8, 21/16, 231/160, 847/640, 2541/2048, ...
CROSSREFS
KEYWORD
nonn,easy,frac
AUTHOR
Wolfdieter Lang, Jun 21 2011
STATUS
approved