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A067374 Integers expressible as the sum of (at least two) consecutive primes in at least 4 ways.

%I A067374 #16 Aug 11 2024 14:41:34
%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 Donovan Johnson, <a href="/A067374/b067374.txt">Table of n, a(n) for n = 1..1000</a>
%H A067374 P. De Geest, <a href="https://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>
%F A067374 A084143(a(n)) > 3. - _Ray Chandler_, Sep 20 2023
%e A067374 E.g., 311 = 101 + 103 + 107 = 53 + 59 + 61 + 67 + 71 = 31 + 37 + 41 + 43 + 47 + 53 + 59 = 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47.
%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] (* _Vladimir Joseph Stephan Orlovsky_, Aug 15 2009 *)
%Y A067374 Cf. A050936, A067372-A067381, A054999.
%K A067374 nonn
%O A067374 1,1
%A A067374 _Patrick De Geest_, Feb 04 2002
%E A067374 Offset corrected by _Donovan Johnson_, Nov 14 2013