A271727 Decimal expansion of the density of exponentially 2^n-numbers (A138302).

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

Offset

0,1

Links

Juan Arias-de-Reyna, Table of n, a(n) for n = 0..1000

Vladimir Shevelev, Exponentially S-numbers, arXiv:1510.05914 [math.NT], 2015-2016.

Vladimir Shevelev, A fast computation of density of exponentially S-numbers, arXiv:1602.04244 [math.NT], 2016.

Formula

Equals Product_{prime p} f(1/p), where f(x) = 1-x^3+Sum_{n>=2}(x^(2^n)-x^(1+2^n)).

Example

0.87249717935391281355800771433253186691958393977733373765412...

Mathematica

$MaxExtraPrecision = m = 500; em = 10; f[x_] := Log[1 - x^3 + Sum[x^(2^e) - x^(1 + 2^e), {e, 2, em}]]; c = Rest[CoefficientList[Series[f[x], {x, 0, m}], x]*Range[0, m]]; RealDigits[Exp[NSum[Indexed[c, k]*PrimeZetaP[k]/k, {k, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 105][[1]] (* Amiram Eldar, Sep 09 2022 *)

Crossrefs

Density of A138302.

Cf. A271726 (Expansion of log(f(x))).

Sequence in context: A328895 A154846 A173598 * A154164 A021538 A179044

Adjacent sequences: A271724 A271725 A271726 * A271728 A271729 A271730

Keyword

nonn,cons

Author

Juan Arias-de-Reyna, Apr 13 2016

Status

approved