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a(1)=1; a(n)=a(n-1)*(number of decimal digits of a(n-1))+1.
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%I #7 Sep 16 2015 13:37:38

%S 1,2,3,4,5,6,7,8,9,10,21,43,87,175,526,1579,6317,25269,126346,758077,

%T 4548463,31839242,254713937,2292425434,22924254341,252166797752,

%U 3026001573025,39338020449326,550732286290565,8260984294358476

%N a(1)=1; a(n)=a(n-1)*(number of decimal digits of a(n-1))+1.

%F a(n) = a(n-1)*floor(log(a(n-1)) + 1) + 1.

%t a = {1}; Do[AppendTo[a, a[[ -1]]*Length[IntegerDigits[a[[ -1]]]] + 1], {40}]; a (* _Stefan Steinerberger_, Jan 30 2008 *)

%K nonn,base

%O 1,2

%A _Rolf Pleisch_, Jan 28 2008

%E More terms from _Stefan Steinerberger_, Jan 30 2008