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%I #20 Apr 03 2023 10:36:11
%S 8,1,4,5,9,6,5,7,1,7,0,2,9,7,2,8,4,5,2
%N Decimal expansion of Sum 1/q, where q is any prime of the form m^2 + 1.
%C The sum is trivially convergent because each term is less than the corresponding term of Sum_{j>=1} 1/(j^2) = (Pi^2)/6.
%C Eight significant digits of this constant are mentioned in A083844, which gives the number of primes of the form m^2 + 1 < 10^n.
%H G. L. Honaker Jr. and C. Caldwell, <a href="https://t5k.org/curios/page.php?number_id=3508">0.81459657</a>, Prime Curios!.
%H Marek Wolf, <a href="http://arxiv.org/abs/0803.1456">Search for primes of the form m^2+1</a>, arXiv:0803.1456 [math.NT], 2008-2010, pp. 6-8.
%F 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 + ...
%e 0.8145965717029728452...
%Y Cf. A002496, A005597.
%K nonn,cons,more
%O 0,1
%A _Jonathan Vos Post_, Jan 28 2010
%E Leading zero removed and offset adjusted by _R. J. Mathar_, Jan 30 2010
%E Corrected and extended by _Robert Gerbicz_, Mar 13 2010
%E Name improved by _T. D. Noe_, Mar 29 2010
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