This site is supported by donations to The OEIS Foundation.

The October issue of the Notices of the Amer. Math. Soc. has an article about the OEIS.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A085964 Decimal expansion of the prime zeta function at 4. 22
 0, 7, 6, 9, 9, 3, 1, 3, 9, 7, 6, 4, 2, 4, 6, 8, 4, 4, 9, 4, 2, 6, 1, 9, 2, 9, 5, 9, 3, 3, 1, 5, 7, 8, 7, 0, 1, 6, 2, 0, 4, 1, 0, 5, 9, 7, 1, 4, 8, 4, 3, 1, 9, 0, 2, 6, 4, 9, 3, 8, 0, 0, 8, 8, 5, 9, 2, 1, 6, 5, 7, 0, 4, 8, 7, 5, 6, 4, 2, 0, 6, 5, 1, 0, 3, 3, 3, 1, 0, 6, 7, 8, 5, 3, 9, 6, 2, 8, 9, 5, 4, 2, 0, 2, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Mathar's Table 1 (cited below) lists expansions of the prime zeta function at integers s in 10..39. - Jason Kimberley, Jan 05 2017 REFERENCES J. W. L. Glaisher, On the Sums of Inverse Powers of the Prime Numbers, Quart. J. Math. 25, 347-362, 1891. LINKS Jason Kimberley, Table of n, a(n) for n = 0..1603 H. Cohen, High Precision Computation of Hardy-Littlewood Constants, Preprint. X. Gourdon and P. Sebah, Some Constants from Number theory R. J. Mathar, Series of reciprocal powers of k-almost primes, arXiv:0803.0900 [math.NT], 2008-2009. Table 1. Eric Weisstein's World of Mathematics, Prime Zeta Function FORMULA P(4) = Sum_{p prime>=2} 1/p^4 = Sum_{n>=1} mobius(n)*log(zeta(4*n))/n Equals A086034 + A085993 + 1/16. [R. J. Mathar, Jul 22 2010] EXAMPLE 0.0769931397642468449426... MAPLE A085964:= proc(i) print(evalf(add(1/ithprime(k)^4, k=1..i), 100)); end: A085964(100000); # Paolo P. Lava, May 29 2012 MATHEMATICA s[n_] := s[n] = Sum[ MoebiusMu[k]*Log[Zeta[4*k]]/k, {k, 1, n}] // RealDigits[#, 10, 104]& // First // Prepend[#, 0]&; s[100]; s[n = 200]; While[s[n] != s[n - 100], n = n + 100]; s[n] (* Jean-François Alcover, Feb 14 2013 *) RealDigits[ PrimeZetaP[ 4], 10, 111][[1]] (* Robert G. Wilson v, Sep 03 2014 *) PROG (MAGMA) R := RealField(106); PrimeZeta := func; [0]cat Reverse(IntegerToSequence(Floor(PrimeZeta(4, 87)*10^105))); // Jason Kimberley, Dec 30 2016 CROSSREFS Decimal expansion of the prime zeta function: A085548 (at 2), A085541 (at 3), this sequence (at 4), A085965 (at 5) to A085969 (at 9). Cf. A013662. Sequence in context: A201766 A197588 A021569 * A281313 A082121 A215338 Adjacent sequences:  A085961 A085962 A085963 * A085965 A085966 A085967 KEYWORD cons,easy,nonn AUTHOR Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jul 06 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 22 22:42 EDT 2018. Contains 315270 sequences. (Running on oeis4.)