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RealDigits[2/NProduct[1 - 1/2^(2^k), {k, 0, Infinity}, WorkingPrecision -> 120] - 3][[1]] (* Amiram Eldar, Feb 19 2024 *)
(PARI) 2/prodinf(k = 0, 1 - 1/2^(2^k)) - 3 \\ Amiram Eldar, Feb 19 2024
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Decimal expansion of 2*Sum_{k>=0} 1/Prod_Product_{i=0..k} (2^(2^i) - 1).
approved
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12.35564270285481672333326271459073955233988293859948777112854057096334466665254291814791046797658771989754
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editing
approved