A244110 Continued fraction expansion of the prime zeta function at 5.

0, 27, 1, 30, 2, 1, 5, 1, 3, 2, 2, 7, 1, 2, 12, 1, 1, 23, 1, 3, 1, 6, 1, 3, 16, 1, 1, 1, 4, 3, 3, 5, 1, 2, 1, 1, 7, 5, 1, 3, 1, 1, 1, 28, 14, 3, 3, 1, 6, 18, 11, 7, 1, 29, 1, 1, 2, 10, 1, 6, 1, 1, 8, 2, 303, 3, 1, 2, 1, 61, 1, 11, 1, 10, 10, 1, 1, 2, 1, 1, 45, 19, 1, 1, 1, 6, 1, 1, 2, 4, 1

Offset

0,2

Comments

Continued fraction of Sum_{n>=1} 1/prime(n)^5 = 0.0357550174839242571328...

Links

Table of n, a(n) for n=0..90.

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

1/2^5 + 1/3^5 + 1/5^5 +1/7^5 + 1/11^5 + 1/13^5 +... = 1/(27 + 1/(1 + 1/(30 + 1/(2 + 1/(1 + 1/(5 + 1/(1 + 1/(3 + 1/...)))))))).

Mathematica

ContinuedFraction[PrimeZetaP[5], 90]

Crossrefs

Cf. A013681, A085965.

Sequence in context: A040753 A040754 A059952 * A338659 A040755 A261197

Adjacent sequences: A244107 A244108 A244109 * A244111 A244112 A244113

Keyword

nonn,cofr

Author

Ilya Gutkovskiy, Dec 16 2015

Status

approved