A347178 Decimal expansion of imaginary part of (i + (i + (i + (i + ...)^(1/3))^(1/3))^(1/3))^(1/3), where i is the imaginary unit.

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

Offset

0,1

Links

Table of n, a(n) for n=0..109.

Eric Weisstein's World of Mathematics, Nested Radical

Formula

Equals -sinh(log((-3*sqrt(3) + sqrt(31))/2)/3)/sqrt(3). - Vaclav Kotesovec, Sep 29 2024

Example

0.3411639019140096636847418698555241284...

Mathematica

RealDigits[((29 + 3 Sqrt[93])^(1/3) - 2^(1/3))/(2 (3 (9 + Sqrt[93]))^(1/3)), 10, 110][[1]]

Prog

(PARI) ((29 + 3*sqrt(93))^(1/3) - 2^(1/3))/(2*(3*(9 + sqrt(93)))^(1/3)) \\ Michel Marcus, Aug 21 2021

Crossrefs

Cf. A060006, A156548, A156590, A347177.

Sequence in context: A073366 A001086 A105283 * A123019 A226063 A326748

Adjacent sequences: A347175 A347176 A347177 * A347179 A347180 A347181

Keyword

nonn,cons

Author

Ilya Gutkovskiy, Aug 21 2021

Status

approved