A265823 Continued fraction expansion of the prime zeta function at 2.

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

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..84.

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

1/2^2 + 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/…))))))).

Mathematica

ContinuedFraction[PrimeZetaP[2], 84]

Crossrefs

Cf. A085548, A013679.

Sequence in context: A338000 A030420 A133902 * A305717 A208645 A361381

Adjacent sequences: A265820 A265821 A265822 * A265824 A265825 A265826

Keyword

nonn,cofr

Author

Ilya Gutkovskiy, Dec 16 2015

Status

approved