A345295 Decimal expansion of Product_{p primes} (1 - 1/p)*(1 + (1 - 1/p^2)*Sum_{k>=1} 1/(p^k + p^(-k-1))).

8, 0, 1, 4, 6, 9, 6, 9, 3, 4, 2, 7, 5, 7, 7, 3, 3, 6, 2, 2, 4, 7, 0, 4, 9, 3, 8, 6, 8, 1, 6, 9, 8, 5, 0, 7, 3, 2, 7, 9, 0, 5, 8, 3, 3, 0, 9, 3, 6, 3, 2, 1, 9, 6, 2, 8, 9, 9, 8, 2, 7, 7, 6, 3, 9, 4, 4, 3, 2, 9, 7, 1, 9, 3, 2, 0, 2, 4, 0, 9, 9, 6, 5, 4, 8, 6, 6, 9, 3, 9, 0, 8, 5, 4, 6, 9, 3, 7, 2, 2, 7, 2, 8, 9, 2, 2

Offset

0,1

Links

Table of n, a(n) for n=0..105.

Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 155 (constant C2).

Vaclav Kotesovec, Plot of 1/n * Sum_{k=1..n} k*A000010(k)/A057660(k) for n = 1..100000

Formula

Equals lim_{n->infinity} 1/n * Sum_{k=1..n} k*A000010(k)/A057660(k).

Example

0.80146969342757733622470493868169850732790583309363219628998277639443297...

Mathematica

$MaxExtraPrecision = 1000; m = 500; Do[Clear[f]; f[p_] := (1 - 1/p)*(1 + (1 - 1/p^2)*Sum[1/(p^j + p^(-j - 1)), {j, 1, k}]); cc = Rest[CoefficientList[Series[Log[f[1/x]], {x, 0, m}], x, m + 1]]; Print[f[2]*Exp[N[Sum[Indexed[cc, n]*(PrimeZetaP[n] - 1/2^n), {n, 2, m}], 110]]], {k, 100, 500, 100}]

Crossrefs

Cf. A057660, A174405, A345294.

Sequence in context: A250219 A037448 A011470 * A198940 A321107 A198117

Adjacent sequences: A345292 A345293 A345294 * A345296 A345297 A345298

Keyword

nonn,cons

Author

Vaclav Kotesovec, Jun 13 2021

Status

approved