A359187 Decimal expansion of the real part of (-sqrt(2))^^9, where ^^ indicates tetration or hyper-4 (e.g., 2^^4 = 2^(2^(2^2))).

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 9, 9, 4, 1, 7, 5, 2, 6, 5, 5, 0, 1, 4, 7, 5, 0, 5, 2, 6, 9, 1, 3, 4, 6, 3, 9, 1, 3, 5, 4, 1, 2, 8, 6, 7, 6, 7, 4, 5, 4, 0

Offset

1,46

Comments

This is the real part of (-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2)).

For a detailed explanation of the fact that a(2) = a(3) = a(4) = ... = a(45), see Links (i.e., the answer provided by the MathOverflow user Saúl RM).

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

MathOverflow, The 9th tetration of -sqrt(2)

Thomas Scheuerle, X: the tetration exponent of (-sqrt(2))^^X; Y: The phase angle of the complex result in units of Pi.

Thomas Scheuerle, X: the tetration exponent of (-sqrt(2))^^X; Y: The absolute value of the complex result.

Example

1.000000000000000000000000000000000000000000004994175...

Maple

b:= n-> `if`(n=0, 1, (-sqrt(2))^b(n-1)):
evalf(Re(b(9)), 130);  # Alois P. Heinz, Nov 24 2023

Mathematica

First[RealDigits[Re[Nest[(-Sqrt[2])^#&, -Sqrt[2], 8]], 10, 100]] (* Paolo Xausa, Oct 24 2023 *)

Prog

(PARI) localprec(100); real((-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))) \\ Michel Marcus, Dec 20 2022

Crossrefs

Cf. A002193, A198094, A365937.

Sequence in context: A145431 A196516 A021671 * A203140 A011512 A200642

Adjacent sequences: A359184 A359185 A359186 * A359188 A359189 A359190

Keyword

easy,cons,nonn

Author

Marco Ripà, Dec 19 2022

Status

approved