A265823 - OEIS

%I #8 Dec 20 2015 13:54:06

%S 0,2,4,1,2,1,3,1,1,33,1,8,3,3,4,1,1,2,1,38,2,29,12,4,1,6,1,1,1,5,4,9,

%T 4,2,2,5,1,3,1,1,1,7,9,1,7,1,201,5,1,17,4,1,19,5,2,56,1,5,1,16,4,1,1,

%U 12,63,1,5,9,1,1,18,26,1,1,5,4,3,1,1,13,2,3,3,1,1

%N Continued fraction expansion of the prime zeta function at 2.

%C Continued fraction of Sum_{n>=1} 1/prime(n)^2 = 0.4522474200410654985065...

%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 1/2^2 + 1/3^2 + 1/5^2 +1/7^2 + 1/11^2 + 1/13^2 +... =  1/(2 + 1/(4 + 1/(1 + 1/(2 + 1/(1 + 1/(3 + 1/(1 + 1/(1 + 1/…))))))).

%t ContinuedFraction[PrimeZetaP[2], 84]

%Y Cf. A085548, A013679.

%K nonn,cofr

%O 0,2

%A _Ilya Gutkovskiy_, Dec 16 2015