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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
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
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
KEYWORD
nonn,cons
AUTHOR
Ilya Gutkovskiy, Aug 21 2021
STATUS
approved