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A067377 Primes expressible as the sum of (at least two) consecutive primes in at least 1 way.

%I A067377 #29 Sep 26 2023 09:04:32
%S A067377 5,17,23,31,41,53,59,67,71,83,97,101,109,127,131,139,173,181,197,199,
%T A067377 211,223,233,251,263,269,271,281,311,331,349,353,373,379,401,421,431,
%U A067377 439,443,449,457,463,479,487,491,499,503,523,563,587,593,607,617,631,647,659,661,677,683,691,701,719
%N A067377 Primes expressible as the sum of (at least two) consecutive primes in at least 1 way.
%H A067377 Hans Havermann, <a href="/A067377/b067377.txt">Table of n, a(n) for n = 1..34589</a>
%H A067377 Patrick De Geest, <a href="http://www.worldofnumbers.com/em122.htm">WONplate 122</a>
%H A067377 Hans Havermann, <a href="http://chesswanks.com/num/a067377.txt">List of possible number of consecutive primes for n = 1..293768</a>
%H A067377 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_046.htm">Puzzle 46. Primes expressible as sum of consecutive primes in K ways</a>, The Prime Puzzles and Problems Connection.
%F A067377 Prime(n) such that A307610(n) > 1. - _Ray Chandler_, Sep 21 2023
%e A067377 The prime 83, for example, is the sum of the five consecutive primes 11 + 13 + 17 + 19 + 23.
%e A067377 The prime 2011, for example, is the sum of the eleven consecutive primes 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211. - _Daniel Forgues_, Nov 03 2011
%t A067377 p = {}; Do[a = Table[ Prime[i], {i, n, 150}]; l = Length[a]; k = 2; While[k < l + 1, b = Plus @@@ Partition[a, k]; k++; p = Append[ p, Select[ b, PrimeQ[ # ] &]]], {n, 1, 149}]; Take[ Union[ Flatten[p]], 70]
%t A067377 m=5!; lst={}; Do[p=Prime[a]; Do[p+=Prime[b]; If[PrimeQ[p]&&p<=Prime[m]*3+8,AppendTo[lst,p]],{b,a+1,m+2,1}],{a,m}]; Union[lst] (* _Vladimir Joseph Stephan Orlovsky_, Aug 15 2009 *)
%Y A067377 Cf. A050936, A067372-A067381, A307610.
%Y A067377 Cf. A197227 (primes that are not the sum of consecutive primes).
%K A067377 nonn
%O A067377 1,1
%A A067377 _Patrick De Geest_, Feb 04 2002
%E A067377 Offset changed to 1 by _Hans Havermann_, Oct 07 2018