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

1,1

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.

Formula

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

Mathematica

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 *)

Prog

(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 */

Crossrefs

Cf. A050936, A067372-A067381, A307610.

Sequence in context: A098061 A141898 A054998 * A331031 A171138 A071886

Adjacent sequences: A067375 A067376 A067377 * A067379 A067380 A067381

Keyword

nonn

Author

Patrick De Geest, Feb 04 2002

Status

approved