Search: id:A069887
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%I A069887
%S A069887 1,2,5,7,7,10,14,16,24,16,20,29,39,40,42,39,46,42,44,57,59,55,66,55,57,
%T A069887 70,68,81,86,81,91,109,106,108,119,117,123,118,124,118,120,133,142,147,
%U A069887 164,155,159,164,167,163,177,176,168,171,198,198,201,201,205,206,227
%N A069887 Number of terms in the simple continued fraction expansion for (1+1/n)^n.
%C A069887 lim n -> infinity (1+1/n)^n=e
%C A069887 For any natural number N, limit_{ n->infinity } ((ln(N))^(1/n) + 1/n)^n 
               = e*ln(N). - Alexander R. Povolotsky (pevnev(AT)juno.com), Dec 06 
               2007
%F A069887 Asymptotically it seems that a(n)=C*n*ln(n)) where C=0.84...is closed 
               to the constant described in A055573(n)
%e A069887 The simple continued fraction for (1+1/10)^10 is [2, 1, 1, 2, 5, 1, 128, 
               1, 2, 12, 5, 3, 46, 1, 11, 7] which contains 16 elements, hence a(10)=16.
%Y A069887 Sequence in context: A131688 A096624 A145378 this_sequence A120303 A093413 
               A004099
%Y A069887 Adjacent sequences: A069884 A069885 A069886 this_sequence A069888 A069889 
               A069890
%K A069887 easy,nonn
%O A069887 1,2
%A A069887 Benoit Cloitre (benoit7848c(AT)orange.fr), May 04 2002

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