A356023 Decimal expansion of Sum_{j>=1} 2^^j/2^^(j+1) where ^^ indicates tetration.

7, 5, 0, 2, 4, 4, 1, 4, 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, 0, 0, 0, 0, 0

Offset: 0

Author

Marco Ripà, Jul 23 2022

Keywords

• nonn
• cons

Comments

This series converges quickly and a very good approximation of this constant is given by the first three terms, 2/2^2 + 2^2/2^2^2 + 2^2^2/2^2^2^2 = 3073/4096, since the next term 2^2^2^2/2^2^2^2^2 is about 1/10^19723.4853.

Examples

			0.750244140625...
		

Crossrefs

Cf. A356022.

Programs

Mathematica

RealDigits[Total[Most[(s = NestList[2^# &, 2, 4])]/Rest[s]], 10, 100][[1]] (* Amiram Eldar, Jul 23 2022 *)