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Primes expressible as the sum of (at least two) consecutive primes in at least 2 ways.
4

%I #28 Sep 26 2023 09:05:28

%S 41,83,197,199,223,251,281,311,401,439,491,593,733,857,863,883,941,

%T 983,991,1061,1151,1187,1283,1361,1367,1381,1433,1439,1493,1511,1523,

%U 1553,1607,1753,1801,1823,1901,1951,2011,2027,2099,2111,2179,2203,2267,2357,2393,2417,2579,2647,2689,2731

%N Primes expressible as the sum of (at least two) consecutive primes in at least 2 ways.

%H Jon E. Schoenfield, <a href="/A067378/b067378.txt">Table of n, a(n) for n = 1..10000</a>

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

%H 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 Prime(n) such that A307610(n) > 2. - _Ray Chandler_, Sep 21 2023

%t m=3*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,1}],{a,m}]; lst1=Sort[lst]; lst={}; Do[If[lst1[[n]]==lst1[[n+1]],AppendTo[lst,lst1[[n]]]],{n,Length[lst1]-1}]; Union[lst] (* _Vladimir Joseph Stephan Orlovsky_, Aug 15 2009 *)

%o (PARI) e=2500; for(d=2,e, if(d%2==1,h=d/3,h=d/2); f=floor(2*d/(log(d)*3)); g=0; for(c=1,f,a=0; b=0; forprime(n=prime(c),h+50,a=a+n; b=b+1;if (a==d,g=g+1; if(g>=2&isprime(a),print1(a, ", ")),if(a>d,next(2)))))) /* The parameter g selects the number of ways wanted. - _Robin Garcia_, Jan 11 2011 */

%Y Cf. A050936, A067372-A067381, A307610.

%K nonn

%O 1,1

%A _Patrick De Geest_, Feb 04 2002