%I A035014
%S A035014 4,44,344,3344,33344,433344,3433344,33433344,333433344,3333433344,
%T A035014 43333433344,343333433344,3343333433344,33343333433344,433343333433344,
%U A035014 3433343333433344,43433343333433344,443433343333433344
%N A035014 a(n) contains n digits (either '3' or '4') and is divisible by 2^n.
%C A035014 If (n-1)-th term is divisible by 2^n, then n-th term begins with a 4. 
               If not, then n-th term begins with a 3.
%C A035014 Proof of conjecture that a(n) ends with a(n-1): If a(n) is divisible 
               by 2^n, then a(n) is divisible by 2^(n-1), so a(n)-k*10^(n-1) is 
               divisible by 2^(n-1) for integer k, but if k is first digit of a(n) 
               then a(n)-k*10^(n-1) is an n-1 digit number made up of 3s and 4s 
               and divisible by 2^(n-1) and so must be a(n-1).
%F A035014 a(n)=a(n-1)+10^(n-1)*(4-[a(n-1)/2^(n-1) mod 2]) i.e. a(n) ends with a(n-1).
%Y A035014 Cf. A050620, A050621, A050622, A023402.
%Y A035014 Sequence in context: A074751 A129551 A081078 this_sequence A030987 A043039 
               A002754
%Y A035014 Adjacent sequences: A035011 A035012 A035013 this_sequence A035015 A035016 
               A035017
%K A035014 nonn,base
%O A035014 1,1
%A A035014 J. Lowell (jhbubby(AT)avana.net)
%E A035014 Corrected and extended by Patrick De Geest (pdg(AT)worldofnumbers.com), 
               Jun 15 1999.
%E A035014 Formula, proof of conjecture and more terms from Henry Bottomley (se16(AT)btinternet.com), 
               Feb 14 2000