%I #16 Aug 11 2024 14:41:34

%S 240,287,311,340,371,510,660,803,863,864,931,961,990,1012,1060,1099,

%T 1104,1151,1164,1236,1313,1320,1367,1392,1524,1643,1650,1710,1788,

%U 1793,1854,1951,1956,2040,2303,2304,2387,2393,2436,2507,2556,2586,2647,2670

%N Integers expressible as the sum of (at least two) consecutive primes in at least 3 ways.

%H Donovan Johnson, <a href="/A067373/b067373.txt">Table of n, a(n) for n = 1..1000</a>

%H P. De Geest, <a href="https://www.worldofnumbers.com/em122.htm">WONplate 122</a>

%H C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_046.htm">Puzzle 46</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeSums.html">Prime Sums</a>

%F A084143(a(n)) > 2. - _Ray Chandler_, Sep 20 2023

%e 240 = (113 + 127) = (53 + 59 + 61 + 67) = (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43) or (#2,113) (#4,53) (#8,17).

%t m=3*5!; lst={}; Do[p=Prime[a]; Do[p+=Prime[b]; If[p<Prime[m]*3+8,AppendTo[lst,p]],{b,a+1,m,1}],{a,m}]; lst1=Sort[lst]; lst={}; Do[If[lst1[[n]]==lst1[[n+1]]&&lst1[[n]]==lst1[[n+2]],AppendTo[lst,lst1[[n]]]],{n,Length[lst1]-2}]; Union[lst] (* _Vladimir Joseph Stephan Orlovsky_, Aug 15 2009 *)

%Y Cf. A050936, A067372-A067381, A054998.

%K nonn

%O 1,1

%A _Patrick De Geest_, Feb 04 2002

%E Offset corrected by _Donovan Johnson_, Nov 14 2013