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Decimal expansion of 2*Sum_{k>=0} 1/Product_{i=0..k} (2^(2^i) - 1).
3

%I #14 Feb 19 2024 02:08:47

%S 2,7,1,1,2,8,5,4,0,5,7,0,9,6,3,3,4,4,6,6,6,6,5,2,5,4,2,9,1,8,1,4,7,9,

%T 1,0,4,6,7,9,7,6,5,8,7,7,1,9,8,9,7,5,4,5,6,9,3,7,9,5,7,1,7,0,6,7,9,5,

%U 0,1,8,9,9,9,5,5,4,4,2,8

%N Decimal expansion of 2*Sum_{k>=0} 1/Product_{i=0..k} (2^(2^i) - 1).

%F From _Amiram Eldar_, Feb 19 2024: (Start)

%F Equals 2 * A258714.

%F Equals 2/A215016 - 3. (End)

%e 2.7112854057096334466665254291814791046797658771989754...

%t RealDigits[2/NProduct[1 - 1/2^(2^k), {k, 0, Infinity}, WorkingPrecision -> 120] - 3][[1]] (* _Amiram Eldar_, Feb 19 2024 *)

%o (PARI) 2/prodinf(k = 0, 1 - 1/2^(2^k)) - 3 \\ _Amiram Eldar_, Feb 19 2024

%Y Cf. A215016, A258714, A258716.

%K nonn,cons

%O 1,1

%A _N. J. A. Sloane_, Jun 15 2015