A265823 - OEIS

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A265823

Continued fraction expansion of the prime zeta function at 2.

0

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

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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