A094965 - OEIS

%I #13 Mar 21 2018 06:32:39

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

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

%U 9,5,2,8,2,3,9,3,0,3,6,9,0,3,6,8,5,4,9,8,8,0,3,4,3,9,5,3,3,0,1,1,6,9,8,8,1

%N A continued fraction transformation of e.

%C The terms of the continued fraction representation of this constant (2.126671411...) are the decimal digits of e.

%C When trying to recover the digits of e from this continued fraction, one gets 2, 7, 1, 8, 2, 8, 1, 8, 2, 8, 4, 5, 13, 5, ... whereas e is 2.718281828459045...; recovered "digits" (sometimes greater than 9) that do not match the actual decimal digits of e occur around places where the actual digits include a 0. E.g., the "904" substring in the actual digits of e results in a recovered "digit" of 9+4 = 13. - _Michel Marcus_ and _Jon E. Schoenfield_, Mar 16 2018

%e 2.126671411...

%t RealDigits[ FromContinuedFraction[ RealDigits[E, 10, 125][[1]]], 10, 111][[1]]

%Y Cf. A001113.

%K cons,easy,nonn,base

%O 1,1

%A _Robert G. Wilson v_, May 26 2004