OFFSET
0,1
COMMENTS
The sum is trivially convergent because each term is less than the corresponding term of Sum_{j>=1} 1/(j^2) = (Pi^2)/6.
Eight significant digits of this constant are mentioned in A083844, which gives the number of primes of the form m^2 + 1 < 10^n.
LINKS
G. L. Honaker Jr. and C. Caldwell, 0.81459657, Prime Curios!.
Marek Wolf, Search for primes of the form m^2+1, arXiv:0803.1456 [math.NT], 2008-2010, pp. 6-8.
FORMULA
Sum_{q in {primes of form m^2 + 1}} 1/q = Sum_{j>=1} 1/A002496(j) = 1/2 + 1/5 + 1/17 + 1/37 + 1/101 + ...
EXAMPLE
0.8145965717029728452...
CROSSREFS
KEYWORD
AUTHOR
Jonathan Vos Post, Jan 28 2010
EXTENSIONS
Leading zero removed and offset adjusted by R. J. Mathar, Jan 30 2010
Corrected and extended by Robert Gerbicz, Mar 13 2010
Name improved by T. D. Noe, Mar 29 2010
STATUS
approved