A347178 - OEIS

%I #9 Sep 29 2024 06:56:42

%S 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,

%T 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,

%U 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

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NestedRadical.html">Nested Radical</a>

%F Equals -sinh(log((-3*sqrt(3) + sqrt(31))/2)/3)/sqrt(3). - _Vaclav Kotesovec_, Sep 29 2024

%e 0.3411639019140096636847418698555241284...

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

%o (PARI) ((29 + 3*sqrt(93))^(1/3) - 2^(1/3))/(2*(3*(9 + sqrt(93)))^(1/3)) \\ _Michel Marcus_, Aug 21 2021

%Y Cf. A060006, A156548, A156590, A347177.

%K nonn,cons

%O 0,1

%A _Ilya Gutkovskiy_, Aug 21 2021