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A345294 Decimal expansion of Product_{p primes} (1 - 1/p)*(1 + (1 + 1/p)*Sum_{k>=1} 1/(p^k + p^(-k-1))). 2
1, 4, 4, 3, 8, 6, 7, 5, 1, 0, 4, 7, 0, 6, 3, 9, 6, 5, 1, 1, 2, 5, 0, 4, 4, 3, 2, 4, 9, 0, 3, 8, 4, 7, 1, 1, 4, 5, 4, 5, 5, 5, 1, 9, 7, 8, 9, 7, 1, 7, 8, 2, 5, 5, 0, 2, 7, 7, 9, 4, 3, 3, 3, 8, 8, 9, 7, 7, 8, 5, 8, 1, 6, 4, 1, 4, 9, 9, 4, 4, 6, 6, 5, 6, 9, 3, 9, 5, 4, 5, 4, 8, 9, 0, 9, 3, 5, 2, 6, 8, 8, 5, 1, 8, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..105.

Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 155 (constant C1).

FORMULA

Equals lim_{n->infinity} 1/n * Sum_{k=1..n} k^2/A057660(k).

EXAMPLE

1.44386751047063965112504432490384711454555197897178255027794333889778581...

MATHEMATICA

$MaxExtraPrecision = 1000; m = 500; Do[Clear[f]; f[p_] := (1 - 1/p)*(1 + (1 + 1/p)*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, A345295.

Sequence in context: A286296 A023530 A337365 * A233581 A193628 A306506

Adjacent sequences:  A345291 A345292 A345293 * A345295 A345296 A345297

KEYWORD

nonn,cons

AUTHOR

Vaclav Kotesovec, Jun 13 2021

STATUS

approved

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Last modified August 1 00:13 EDT 2021. Contains 346377 sequences. (Running on oeis4.)