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

Author

Ilya Gutkovskiy, Aug 21 2021

Keywords

• nonn
• cons

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

Examples

			1.1615413999972519360879176872471740748431...
		

Links

• Eric Weisstein's World of Mathematics, Nested Radical

Crossrefs

Cf. A060006, A156548, A156590, A347178.

Programs

Mathematica

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

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

Formula

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