Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Dec 20 2015 13:54:34
%S 0,5,1,2,1,1,2,17,4,1,7,1,1,5,24,1,1,2,3,11,1,3,23,1,1,2,1,3,1,6,1,4,
%T 3,3,1,2,1,4,1,1,3,1,1,1,2,23,2,6,2,2,1,1,7,3,13,1,1,2,6,1,5,5,1,2,1,
%U 1,1,1,2,1,3,1,28,2,1,4,10,3,2,1,1,2,1,3,1,1
%N Continued fraction expansion of the prime zeta function at 3.
%C Continued fraction of Sum_{n>=1} 1/prime(n)^3 = 0.1747626392994435364231...
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeZetaFunction.html">Prime Zeta Function</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Prime_zeta_function">Prime Zeta Function</a>
%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%H <a href="/index/Z#zeta_function">Index entries for zeta function</a>
%e 1/2^3 + 1/3^3 + 1/5^3 +1/7^3 + 1/11^3 + 1/13^3 +... = 1/(5 + 1/(1 + 1/(2 + 1/(1 + 1/(1 + 1/(2 + 1/(17 + 1/(4 + 1/…)))))))).
%t ContinuedFraction[PrimeZetaP[3], 85]
%Y Cf. A085541, A013631.
%K nonn,cofr
%O 0,2
%A _Ilya Gutkovskiy_, Dec 16 2015