A347177 Decimal expansion of real part of (i + (i + (i + (i + ...)^(1/3))^(1/3))^(1/3))^(1/3), where i is the imaginary unit.

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

Offset

1,3

Comments

This is the sum of the imaginary parts of the complex roots of the cubic equation 8*r^3 + 2*r - 1 = 0 , and its real solution is A347178. - Gerry Martens, Apr 02 2024

Links

Table of n, a(n) for n=1..110.

Eric Weisstein's World of Mathematics, Nested Radical

Formula

Equals cosh(asinh(3*sqrt(3)/2)/3). - Gerry Martens, Apr 02 2024

Example

1.1615413999972519360879176872471740748431...

Mathematica

RealDigits[(1/12) 2^(2/3) 3^(5/6) ((Sqrt[93] - 9)^(1/3) + (9 + Sqrt[93])^(1/3)), 10, 110][[1]]

Prog

(PARI) (1/12)*2^(2/3)*3^(5/6)*((sqrt(93) - 9)^(1/3) + (9 + sqrt(93))^(1/3)) \\ Michel Marcus, Aug 21 2021
(PARI) 2*imag(polroots(8*x^3 + 2*x - 1)[3]) \\ Gerry Martens, Apr 02 2024

Crossrefs

Cf. A060006, A156548, A156590, A347178.

Sequence in context: A212006 A245725 A011096 * A195695 A199047 A021623

Adjacent sequences: A347174 A347175 A347176 * A347178 A347179 A347180

Keyword

nonn,cons

Author

Ilya Gutkovskiy, Aug 21 2021

Status

approved