A211342 Decimal expansion of q between 0 and 1 maximizing Dedekind eta function eta(q) = q^(1/24) * Product_{n>=1} (1 - q^n).

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

Offset

0,2

Links

Table of n, a(n) for n=0..100.

Eric Weisstein's MathWorld, Dedekind Eta Function

Formula

Root of the equation Sum_{k>=1} A000203(k) * r^k = 1/24. - Vaclav Kotesovec, Jun 28 2017

Equals A057823^2. - Vaclav Kotesovec, Jul 02 2017

Example

0.0372768102964516581509807856516446180362823794827830067...

Mathematica

q /. Last @ FindMaximum[ DedekindEta[ -I*Log[q]/(2*Pi)], {q, 1/25}, WorkingPrecision -> 200] // RealDigits[#][[1]][[1 ;; 100]]& // Prepend[#, 0]&
x /. FindRoot[24*Sum[DivisorSigma[1, k]*x^k, {k, 1, 1000}] == 1, {x, 1}, WorkingPrecision -> 101] (* Vaclav Kotesovec, Jun 28 2017 *)

Crossrefs

Cf. A000203, A057823, A288877, A289392.

Sequence in context: A246201 A279341 A254155 * A363940 A199401 A261573

Adjacent sequences: A211339 A211340 A211341 * A211343 A211344 A211345

Keyword

nonn,cons

Author

Jean-François Alcover, Feb 05 2013

Status

approved