%I A110700
%S A110700 1,0,0,1,0,3,0,1,1,1,1,1,0,3,1,1,0,1,0,1,1,2,1,1,1,2,1,1,1,3,0,1,1,1,1,
%T A110700 2,1,2,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,2,1,1,2,1,1,1,0,3,1,1,1,1,1,1,1,2,
%U A110700 1,1,1,1,1,1,1,2,1,1,2,1,1,1,1,1,1,1,0,2,1,1,1,2,1,1,1,1,1,1
%N A110700 Number of zeros in the smallest prime with Hamming weight n (given by 
               A061712).
%C A110700 a(n)=0 iff n belongs A000043.
%C A110700 Observe that a(n)=3 for n=6, 14, 30, 62, 126, 254, 510, 1022, ... which 
               is A000918. Conjecture: a(n) is never greater than 3. - T. D. Noe, 
               Mar 14 2008
%H A110700 T. D. Noe, <a href="b110700.txt">Table of n, a(n) for n=1..1024</a>
%F A110700 A110700(n) = A110699(n) - n
%p A110700 with(combstruct); a:=proc(n) local m,is,s,t,r; if n=1 then return 1 fi; 
               r:=+infinity; for m from 0 do is := iterstructs(Combination(n-2+m),
               size=n-2); while not finished(is) do s := nextstruct(is); t := 2^(n-1+m)+1+add(2^i,
               i=s); if isprime(t) then return m fi; od; od; return 0; end;
%Y A110700 Cf. A000043, A061712, A110699.
%Y A110700 Sequence in context: A101949 A124796 A065714 this_sequence A051908 A056614 
               A092510
%Y A110700 Adjacent sequences: A110697 A110698 A110699 this_sequence A110701 A110702 
               A110703
%K A110700 nonn
%O A110700 1,6
%A A110700 Max Alekseyev (maxale(AT)gmail.com), Aug 03 2005