%I A067374
%S A067374 311,863,1164,1320,1650,1854,2856,2867,3198,3264,3754,4200,4920,5100,
%T A067374 5770,5999,6504,8152,10134,10320,10536,10649,11058,12294,12438,12762,
%U A067374 12820,12954,12990,14369,14699,14826,15329,15610,15762,16199,16277
%N A067374 Integers expressible as the sum of (at least two) consecutive primes 
               in at least 4 ways.
%H A067374 P. De Geest, <a href="http://www.worldofnumbers.com/em122.htm">WONplate 
               122</a>
%H A067374 C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_046.htm">
               Puzzle 46</a>
%e A067374 E.g. 311 = (#3,101) (#5,53) (#7,31) (#11,11).
%t A067374 Clear[lst,lst1,m,n,p,a,b] m=2*6!; lst={}; Do[p=Prime[a]; Do[p+=Prime[b]; 
               If[p<Prime[m]*2+3,AppendTo[lst,p]],{b,a+1,m+2,1}],{a,m}]; lst1=Sort[lst]; 
               lst={}; Do[If[lst1[[n]]==lst1[[n+1]]&&lst1[[n]]==lst1[[n+2]]&&lst1[[n]]==lst1[[n+3]],
               AppendTo[lst,lst1[[n]]]],{n,Length[lst1]-3}]; Union[lst] [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Aug 15 2009]
%Y A067374 Cf. A050936, A067372-A067381, A054999.
%Y A067374 Sequence in context: A142576 A025024 A067379 this_sequence A055000 A067380 
               A046495
%Y A067374 Adjacent sequences: A067371 A067372 A067373 this_sequence A067375 A067376 
               A067377
%K A067374 nonn
%O A067374 0,1
%A A067374 Patrick De Geest (pdg(AT)worldofnumbers.com), Feb 04 2002.