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Decimal expansion of 2^(3/2)^(4/3)^(5/4)^(6/5)^(7/6)^(8/7)^(9/8)^(10/9)^(11/10)....
5

%I #15 Mar 02 2021 18:46:39

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

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

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

%N Decimal expansion of 2^(3/2)^(4/3)^(5/4)^(6/5)^(7/6)^(8/7)^(9/8)^(10/9)^(11/10)....

%C I do not use brackets for the powers, so do not confuse this with 2^(3/2*4/3*5/4...)

%C Obtaining 100 digits of precision only requires computing 2^(3/2)^(4/3)^...^(70/69). - _Ryan Propper_, May 06 2006

%e 3.5038099724520171086395374917713267007683... - _Jianing Song_, Nov 18 2018

%t k = 1; For[a = 100, a > 1, a--, k = (a/(a-1))^k]; First[RealDigits[N[k, 100]]] (* _Ryan Propper_, May 06 2006 *)

%Y Cf. A242759, A242760, A341324, A341325.

%K cons,nonn

%O 1,1

%A Raes Tom (tommy1729(AT)hotmail.com), Feb 25 2005

%E More terms from _Ryan Propper_, May 06 2006