A270915 Decimal expansion of a constant related to the asymptotics of A008485.

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

Offset

1,1

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..500

Formula

Equals limit n->infinity A008485(n)^(1/n).

Example

5.352701333486642687772415814165327879851483271286947097319690756...

Mathematica

RealDigits[1/r /. FindRoot[{s == 1/QPochhammer[r*s], QPochhammer[r*s] + r*s*Derivative[0, 1][QPochhammer][r*s, r*s] == (Log[1 - r*s] + QPolyGamma[0, 1, r*s]) / (s*Log[r*s])}, {r, 1/5}, {s, 1}, WorkingPrecision -> 120], 10, 105][[1]] (* Vaclav Kotesovec, Sep 26 2023 *)

Crossrefs

Cf. A008485, A109084, A109085, A206228, A270914, A303070, A304625, A327279.

Sequence in context: A194624 A239805 A333236 * A319461 A201762 A153386

Adjacent sequences: A270912 A270913 A270914 * A270916 A270917 A270918

Keyword

nonn,cons

Author

Vaclav Kotesovec, Mar 25 2016

Status

approved