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A356023
Decimal expansion of Sum_{j>=1} 2^^j/2^^(j+1) where ^^ indicates tetration.
1
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
0,1
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.
EXAMPLE
0.750244140625...
MATHEMATICA
RealDigits[Total[Most[(s = NestList[2^# &, 2, 4])]/Rest[s]], 10, 100][[1]] (* Amiram Eldar, Jul 23 2022 *)
CROSSREFS
Cf. A356022.
Sequence in context: A277067 A354823 A241902 * A113223 A096414 A144923
KEYWORD
nonn,cons
AUTHOR
Marco Ripà, Jul 23 2022
STATUS
approved