The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A238734 Log of twice the twin prime constant, C_2, log(2*A005597). 0
 2, 7, 7, 8, 7, 6, 8, 8, 2, 0, 7, 3, 2, 3, 1, 9, 6, 1, 9, 3, 2, 3, 1, 0, 8, 6, 6, 7, 0, 3, 2, 5, 3, 4, 2, 0, 3, 6, 0, 2, 0, 6, 2, 9, 4, 1, 4, 7, 3, 6, 8, 2, 9, 8, 8, 2, 4, 5, 2, 7, 0, 5, 3, 3, 6, 7, 7, 1, 6, 4, 9, 8, 0, 0, 8, 2, 8, 3, 5, 0, 7, 5, 9, 9, 6, 6, 3, 7, 4, 8, 8, 4, 6, 9, 1, 0, 3, 9, 4, 1, 6, 6, 9, 8, 0, 9, 2, 9, 5, 8, 6, 6, 1 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The value occurs as term in equation (15) in the Wolf paper. - Ralf Stephan, Mar 28 2014 LINKS Marek Wolf, Nearest-neighbor-spacing distribution of prime numbers and quantum chaos, arXiv:1212.3841 [math.NT], 2012-2014. Marek Wolf, Nearest-neighbor-spacing distribution of prime numbers and quantum chaos, Phys. Rev. E 89, 022922 (2014). FORMULA log(2*A005597). EXAMPLE 0.2778768820732319619323108667032534203602062941473682988245270533677164980... MATHEMATICA digits = 113; s[n_] := (1/n)*N[Sum[MoebiusMu[d]*2^(n/d), {d, Divisors[n]}], digits + 50]; C2 = (175/256)*Product[(Zeta[n]*(1 - 2^(-n))*(1 - 3^(-n))*(1 - 5^(-n))*(1 - 7^(-n)))^(-s[n]), {n, 2, digits + 50}]; RealDigits[Log[2 C2]][[1]][[1 ;; digits]] (* Jean-François Alcover, Feb 16 2019 *) PROG (PARI) default(realprecision, 1000); result={175/256*prod(k=2, 500, (zeta(k)*(1-1/2^k)*(1-1/3^k)*(1-1/5^k)*(1-1/7^k))^(-sumdiv(k, d, moebius(d)*2^(k/d))/k))}; log(2*result) CROSSREFS Cf. A005597, A114907. Sequence in context: A246553 A330479 A257960 * A316352 A114532 A003061 Adjacent sequences:  A238731 A238732 A238733 * A238735 A238736 A238737 KEYWORD nonn,cons,less AUTHOR John W. Nicholson, Mar 03 2014 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 26 13:13 EDT 2020. Contains 334626 sequences. (Running on oeis4.)