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approved

Continued fraction expansion of the prime zeta function at 3.

proposed

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proposed

Continued fraction of Sum_{n>=1} 1/prime(n)^3 = 0.1747626392994435364231...

<a href="/index/Con#confC">Index entries for continued fractions for constants</a> <a href="/index/Z#zeta_function">Index entries for zeta function</a>

<a href="/index/Z#zeta_function">Index entries for zeta function</a>

proposed

editing

editing

proposed

ContinuedFraction[PrimeZetaP[3], 12085]

allocated for Ilya GutkovskiyContinued fraction of the prime zeta function at 3.

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, 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, 1, 1, 1, 2, 1, 3, 1, 28, 2, 1, 4, 10, 3, 2, 1, 1, 2, 1, 3, 1, 1

0,2

Continued fraction of Sum_{n>=1} 1/prime(n)^3 = 0.1747626392994435364231...

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeZetaFunction.html">Prime Zeta Function</a>

Wikipedia, <a href="http://en.wikipedia.org/wiki/Prime_zeta_function">Prime Zeta Function</a>

<a href="/index/Con#confC">Index entries for continued fractions for constants</a> <a href="/index/Z#zeta_function">Index entries for zeta function</a>

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/…)))))))).

ContinuedFraction[PrimeZetaP[3], 120]

Cf. A085541, A013631.

allocated

nonn,cofr

Ilya Gutkovskiy, Dec 16 2015

approved

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allocated for Ilya Gutkovskiy

allocated

approved