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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

Table of n, a(n) for n=0..112.

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: A021040 A246553 A257960 * A316352 A114532 A003061

Adjacent sequences:  A238731 A238732 A238733 * A238735 A238736 A238737

KEYWORD

nonn,cons,less,changed

AUTHOR

John W. Nicholson, Mar 03 2014

STATUS

approved

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Last modified February 21 15:11 EST 2019. Contains 320374 sequences. (Running on oeis4.)