A067378 Primes expressible as the sum of (at least two) consecutive primes in at least 2 ways.

41, 83, 197, 199, 223, 251, 281, 311, 401, 439, 491, 593, 733, 857, 863, 883, 941, 983, 991, 1061, 1151, 1187, 1283, 1361, 1367, 1381, 1433, 1439, 1493, 1511, 1523, 1553, 1607, 1753, 1801, 1823, 1901, 1951, 2011, 2027, 2099, 2111, 2179, 2203, 2267, 2357, 2393, 2417, 2579, 2647, 2689, 2731

Offset: 1

Author

Patrick De Geest, Feb 04 2002

Keywords

• nonn

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..10000
• Patrick De Geest, WONplate 122
• Carlos Rivera, Puzzle 46. Primes expressible as sum of consecutive primes in K ways, The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A050936, A067372-A067381, A307610.

Programs

Mathematica

m=3*5!; lst={}; Do[p=Prime[a]; Do[p+=Prime[b]; If[PrimeQ[p]&&pVladimir Joseph Stephan Orlovsky, Aug 15 2009 *)

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 */

Formula

Prime(n) such that A307610(n) > 2. - Ray Chandler, Sep 21 2023