A364806 Decimal expansion of 1/(Re((-sqrt(2))^^9) - 1), where ^^ indicates tetration.

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

Offset

45,1

Comments

This sequence is based on A359187, and was suggested by Thomas Scheuerle on December 19 2022.

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).

Links

Table of n, a(n) for n=45..131.

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

Formula

Equals 1/(Re((-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))^(-sqrt(2))) - 1).

Equals 1/(A359187 - 1).

Example

200233261116755784266797207108302997814593266.829345153326335489937486...

Maple

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

Mathematica

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 *)

Prog

(PARI) default(realprecision, 100); x=1; for(i=1, 9, x=(-sqrt(2))^x); 1/real(x-1) \\ Michal Paulovic, Aug 20 2023

Crossrefs

Cf. A002193, A198094, A359187, A364711, A365937.

Sequence in context: A146095 A230557 A327950 * A024870 A147699 A250023

Adjacent sequences: A364803 A364804 A364805 * A364807 A364808 A364809

Keyword

easy,cons,nonn,less

Author

Marco Ripà and Thomas Scheuerle, Aug 08 2023

Status

approved