A356022 Decimal expansion of the infinite series Sum_{j=0..oo} 1/2^^j where ^^ indicates tetration.

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

Offset

1,2

Comments

This constant converges very fast to a finite value around 118785/65536, since tetration (AKA hyper-4) makes 2^^k become very big so quickly, even for "relatively small" values of k (e.g., 1/2^^5 < 1/10^19728.30).

This sequence has been inspired by a question posted by the user Max Muller on MathOverflow on July 2022 (see Links).

Links

Table of n, a(n) for n=1..87.

MathOverflow, References on infinite series involving the tetration operator, like sum(n=0,infinity)1/2^^n, July 23 2022.

Formula

Equals Sum_{j=0..oo) A014221(j).

Example

1.812515258789...

Mathematica

RealDigits[Total[1/NestList[2^# &, 1, 5]], 10, 100][[1]] (* Amiram Eldar, Jul 23 2022 *)

Crossrefs

Cf. A014221, A356023, A007404.

Sequence in context: A010518 A303321 A368146 * A077464 A088373 A154167

Adjacent sequences: A356019 A356020 A356021 * A356023 A356024 A356025

Keyword

nonn,cons

Author

Marco Ripà, Jul 23 2022

Status

approved