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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.

%I A347178 #10 Feb 16 2025 08:34:02
%S A347178 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 A347178 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 A347178 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 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.
%H A347178 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NestedRadical.html">Nested Radical</a>
%F A347178 Equals -sinh(log((-3*sqrt(3) + sqrt(31))/2)/3)/sqrt(3). - _Vaclav Kotesovec_, Sep 29 2024
%e A347178 0.3411639019140096636847418698555241284...
%t A347178 RealDigits[((29 + 3 Sqrt[93])^(1/3) - 2^(1/3))/(2 (3 (9 + Sqrt[93]))^(1/3)), 10, 110][[1]]
%o A347178 (PARI) ((29 + 3*sqrt(93))^(1/3) - 2^(1/3))/(2*(3*(9 + sqrt(93)))^(1/3)) \\ _Michel Marcus_, Aug 21 2021
%Y A347178 Cf. A060006, A156548, A156590, A347177.
%K A347178 nonn,cons
%O A347178 0,1
%A A347178 _Ilya Gutkovskiy_, Aug 21 2021