A364711 - OEIS

A364711

Decimal expansion of (negative of) the real part of (-sqrt(2))^^10, where ^^ indicates tetration or hyper-4 (e.g., 2^^4 = 2^(2^(2^2))).

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

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OFFSET

1,2

COMMENTS

The real part of (-sqrt(2))^^9 is very close to 1 (see A359187), so the present sequence is about sqrt(2).

In details, we have that 4.275881*10^(-45) < sqrt(2) + Re(-sqrt(2))^^10 < 4.27582*10^(-45).

LINKS

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

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

FORMULA

Equals -Re((-sqrt(2)) ^ (-sqrt(2)) ^ (-sqrt(2)) ^ (-sqrt(2)) ^ (-sqrt(2)) ^ (-sqrt(2)) ^ (-sqrt(2)) ^ (-sqrt(2)) ^ (-sqrt(2)) ^ (-sqrt(2))).

EXAMPLE

1.414213562373095048801688724209698078569671871101066587094934996...

MATHEMATICA

First[RealDigits[Re[Nest[(-Sqrt[2])^#&, -Sqrt[2], 9]], 10, 100]] (* Paolo Xausa, Dec 06 2023 *)

CROSSREFS

Cf. A002193, A359187, A364806, A365937.

Sequence in context: A297420 A156896 A375743 * A002193 A020807 A188582

Adjacent sequences: A364708 A364709 A364710 * A364712 A364713 A364714

KEYWORD

easy,cons,nonn

AUTHOR

Marco Ripà, Oct 20 2023

STATUS

approved