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A365937
Decimal expansion of the real part of (-sqrt(2))^^8, where ^^ indicates tetration or hyper-4 (e.g., 2^^4 = 2^(2^(2^2))).
4
6, 4, 9, 1, 8, 7, 8, 4, 7, 2, 5, 5, 8, 1, 2, 8, 2, 9, 1, 3, 4, 6, 6, 1, 6, 5, 5, 8, 5, 0, 0, 4, 1, 5, 5, 4, 1, 1, 6, 0, 1, 6, 6, 5, 9, 1, 4, 6, 6, 7, 2, 2, 8, 8, 3, 7, 0, 2, 6, 3, 7, 8, 8, 1, 3, 6, 6, 2, 5, 3, 0, 3, 2, 3, 1, 2, 3, 2, 4, 4, 1, 6, 0, 2, 1, 8, 0
OFFSET
-45,1
COMMENTS
This sequence is connected to A359187.
For a detailed explanation of the fact that Re((-sqrt(2))^^9) is surprisingly close to 1, see Links (i.e., the answer provided by the MathOverflow user Saúl RM).
FORMULA
Equals Re((-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))).
EXAMPLE
6.4918784725581282913466165585...*10^(-46)
MATHEMATICA
First[RealDigits[Re[Nest[(-Sqrt[2])^#&, -Sqrt[2], 7]], 10, 100]] (* Paolo Xausa, Oct 24 2023 *)
CROSSREFS
KEYWORD
easy,cons,nonn
AUTHOR
Marco Ripà, Sep 23 2023
STATUS
approved