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%I #7 Mar 30 2012 18:39:05
%S 3,2,4,4,12,3,9,3,5,5,9,5,11,13,15,13,15,4,8,10,14,4,6,4,8,6,10,6,8,
%T 10,12,10,18,6,10,12,14,12,14,14,20,16,18,14,16,14,26,16,24,5,7,9,11,
%U 9,15,11,13,15,17,5,9,5,9,7,9,5,7,9,13,9,11,7,9,11,21,11,15,7,9,9,11,11,17
%N Let c(1)=n, e=2.71... and c(k+1)=floor(c(k)/e) if c(k) is even, c(k+1)=floor(e*c(k)) otherwise; sequence gives the smallest value a(n) such that c(a(n))=0.
%F Conjecture: sequence always exists and there is a constant C=2.9... such that sum(k=1, n, a(k)) is asymptotic to C*n*Log(n). Is this constant the same as those for the sequence involving Pi instead of e?
%o (PARI) P=exp(1); a(n)=if(n<0,0,s=n; t=2; while(floor(s/P^(-1)^s)>0,s=floor(s/P^(-1)^s); t++); t)
%K easy,nonn
%O 1,1
%A _Benoit Cloitre_, Aug 23 2002
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