A265825 Continued fraction expansion of the prime zeta function at 4.

0, 12, 1, 83, 1, 1, 7, 3, 9, 1, 23, 1, 4, 1, 1, 5, 1, 2, 17, 1, 1, 3, 1, 16, 3, 2, 1, 10, 5, 89, 1, 1, 1, 4, 3, 2, 3, 1, 2, 2, 3, 3, 3, 13, 1, 3, 1, 5, 1, 56, 1, 2, 8, 1, 19, 1, 22, 5, 5, 3, 72, 1, 2, 1, 1, 11, 2, 8, 1, 2, 2, 1, 7, 2, 6, 3, 3, 3, 6, 2, 3, 7, 1

Offset

0,2

Comments

Continued fraction of Sum_{n>=1} 1/prime(n)^4 = 0.0769931397642468449426...

Links

Table of n, a(n) for n=0..82.

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

1/2^4 + 1/3^4 + 1/5^4 +1/7^4 + 1/11^4 + 1/13^4 +... = 1/(12 + 1/(1 + 1/(83 + 1/(1 + 1/(1 + 1/(7 + 1/(3 + 1/(9 + 1/...)))))))).

Mathematica

ContinuedFraction[PrimeZetaP[4], 82]

Crossrefs

Cf. A085964, A013680.

Sequence in context: A278468 A280975 A075072 * A347492 A038327 A225750

Adjacent sequences: A265822 A265823 A265824 * A265826 A265827 A265828

Keyword

nonn,cofr

Author

Ilya Gutkovskiy, Dec 16 2015

Status

approved