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%I #3 Mar 30 2012 18:36:39
%S 1,2,4,6,7,8,13,11,12,18,22,20,27,27,24,32,35,34,39,43,44,42,44,53,56,
%T 54,60,67,69,59,72,75,76,72,83,81,87,81,96,99,102,107,108,106,105,112,
%U 114,115,121,130,125,129,125,131,135,152,149,139,139,150,154,161,162
%N a(n) equals the number of partial quotients of the simple continued fraction expansion of the nonsimple continued fraction: 1/(1+2/(2+3/(3+...+n/n)))).
%C The finite nonsimple continued fraction, 1/(1+2/(2+3/(3+...+n/n)))), as n grows, has the limit: 1/(e-1) = [0;1,1,2,1,1,4,1,1,6,...] (A005131).
%e a(5)=7 since there are 7 partial quotients in the resultant simple continued fraction of 1/(1+2/(2+3/(3+4/(4+5/5)))) = 53/91 = [0;1,1,2,1,1,7].
%e The count of partial quotients includes the initial integer position.
%Y Cf. A005131.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Oct 01 2003
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