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%I #17 Aug 11 2024 14:41:34
%S 16277,20272,25416,28500,34421,41074,45101,46660,50560,53424,59068,
%T 68787,70104,70692,71548,78756,85433,85481,88453,94350,98881,105827,
%U 117907,120151,121847,125952,130638,130789,131420,132539,133367,134376,135918,139853,158810
%N Integers expressible as the sum of (at least two) consecutive primes in at least 5 ways.
%H Donovan Johnson, <a href="/A067375/b067375.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>
%F A084143(a(n)) > 4. - _Ray Chandler_, Sep 20 2023
%e E.g. 16277 = (#7,2297) (#11,1451) (#13,1213) (#35,359) (#37,331).
%t t={};Do[p=Prime[m];Do[p=p+Prime[n];If[p<200000,AppendTo[t,p]],{n,m+1,7001}],{m,1,7000}];t=Sort@t;f5[l_]:=Module[{t={}},Do[If[l[[n]]==l[[n+4]],AppendTo[t,l[[n]]]],{n,Length[l]-4}];t];Union@f5[t] (* _Vladimir Joseph Stephan Orlovsky_, Jan 30 2012 *)
%Y Cf. A050936, A067372-A067381, A055000.
%K nonn
%O 1,1
%A _Patrick De Geest_, Feb 04 2002
%E Offset and a(35) corrected by _Donovan Johnson_, Nov 14 2013