A356022 Decimal expansion of the infinite series Sum_{j>=0} 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

Author

Marco Ripà, Jul 23 2022

Keywords

• nonn
• cons

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).

Examples

			1.812515258789...
		

Links

• MathOverflow, References on infinite series involving the tetration operator, like Sum_{n=1..oo} 1/2^^n, July 23 2022.

Crossrefs

Cf. A014221, A356023, A007404.

Programs

Mathematica

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

Formula

Equals Sum_{j>=0} 1/A014221(j).