A265824 Continued fraction expansion 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

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..85.

Eric Weisstein's World of Mathematics, Prime Zeta Function

Wikipedia, Prime Zeta Function

Index entries for continued fractions for constants

Index entries for zeta function

Example

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/…)))))))).

Mathematica

ContinuedFraction[PrimeZetaP[3], 85]

Crossrefs

Cf. A085541, A013631.

Sequence in context: A351241 A273874 A086039 * A097413 A202352 A115038

Adjacent sequences: A265821 A265822 A265823 * A265825 A265826 A265827

Keyword

nonn,cofr

Author

Ilya Gutkovskiy, Dec 16 2015

Status

approved