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%I #4 Mar 31 2012 14:11:37
%S 1,2,33,444444444444444444444444444444444
%N "Que sera, sera" sequence: self-describing sequence where a(n) gives the number of n+1's which will be concatenated to form a(n+1); starting with a(1) = 1.
%F a(1) = 1. For n > 1, let k = floor(1+log_10(n)); then a(n) = n*(10^(k*a(n-1))-1)/(10^k-1).
%e a(1) says: there will be one 2 in a(2).
%e a(2)=2 because a(1) said so; and a(2)=2 says: there will be two 3's in a(3).
%e a(3)=33 because a(2) said so; and also a(3) says: there will be thirty three 4's in a(4).
%e Therefore a(4)= 444444444444444444444444444444444 (33 times the digit 4).
%e And a(5)= 555555555555555...555 (with 444444444444444444444444444444444 5's).
%Y Cf. A001462, A001463, A103320, A102357, A076782.
%K base,nonn
%O 1,2
%A _Alexandre Wajnberg_, Aug 23 2005
%E Formula corrected to handle n>9 also by _Rick L. Shepherd_, Mar 22 2009
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