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%I #52 Jan 09 2024 10:26:58
%S 2,0,0,2,3,3,2,6,1,1,1,6,7,5,5,7,8,4,2,6,6,7,9,7,2,0,7,1,0,8,3,0,2,9,
%T 9,7,8,1,4,5,9,3,2,6,6,8,2,9,3,4,5,1,5,3,3,2,6,3,3,5,4,8,9,9,3,7,4,8,
%U 6,4,3,0,3,6,2,1,4,6,3,7,0,7,8,4,1,1,9
%N Decimal expansion of 1/(Re((-sqrt(2))^^9) - 1), where ^^ indicates tetration.
%C This sequence is based on A359187, and was suggested by _Thomas Scheuerle_ on December 19 2022.
%C For a detailed explanation of the fact that Re((-sqrt(2))^^9) is surprisingly close to 1, because Re((-sqrt(2))^^8) is small at about 6.491878...*10^-46, see Links (i.e., the answer provided by the MathOverflow user Saúl RM).
%H MathOverflow, <a href="https://mathoverflow.net/questions/435085/the-9th-tetration-of-sqrt2/435088#435088">The 9th tetration of -sqrt(2)</a>.
%F Equals 1/(Re((-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))) - 1).
%F Equals 1/(A359187 - 1).
%e 200233261116755784266797207108302997814593266.829345153326335489937486...
%p Digits:=100: 1: for i from 1 to 9 do (-sqrt(2))^% end do: printf("%.55f", 1/Re(evalf[150](%-1))); # _Michal Paulovic_, Aug 20 2023
%t x=1; Do[x=(-Sqrt[2])^x, {9}]; x=1/Re[N[x-1, 100]]; RealDigits[x, 10, 100][[1]] (* _Michal Paulovic_, Aug 20 2023 *)
%o (PARI) default(realprecision, 100); x=1; for(i=1, 9, x=(-sqrt(2))^x); 1/real(x-1) \\ _Michal Paulovic_, Aug 20 2023
%Y Cf. A002193, A198094, A359187, A364711, A365937.
%K easy,cons,nonn,less
%O 45,1
%A _Marco Ripà_ and _Thomas Scheuerle_, Aug 08 2023
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