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A067374
Integers expressible as the sum of (at least two) consecutive primes in at least 4 ways.
2
311, 863, 1164, 1320, 1650, 1854, 2856, 2867, 3198, 3264, 3754, 4200, 4920, 5100, 5770, 5999, 6504, 8152, 10134, 10320, 10536, 10649, 11058, 12294, 12438, 12762, 12820, 12954, 12990, 14369, 14699, 14826, 15329, 15610, 15762, 16199, 16277
OFFSET
1,1
LINKS
P. De Geest, WONplate 122
C. Rivera, Puzzle 46
FORMULA
A084143(a(n)) > 3. - Ray Chandler, Sep 20 2023
EXAMPLE
E.g., 311 = 101 + 103 + 107 = 53 + 59 + 61 + 67 + 71 = 31 + 37 + 41 + 43 + 47 + 53 + 59 = 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47.
MATHEMATICA
Clear[lst, lst1, m, n, p, a, b] m=2*6!; lst={}; Do[p=Prime[a]; Do[p+=Prime[b]; If[p<Prime[m]*2+3, AppendTo[lst, p]], {b, a+1, m+2, 1}], {a, m}]; lst1=Sort[lst]; lst={}; Do[If[lst1[[n]]==lst1[[n+1]]&&lst1[[n]]==lst1[[n+2]]&&lst1[[n]]==lst1[[n+3]], AppendTo[lst, lst1[[n]]]], {n, Length[lst1]-3}]; Union[lst] (* Vladimir Joseph Stephan Orlovsky, Aug 15 2009 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Patrick De Geest, Feb 04 2002
EXTENSIONS
Offset corrected by Donovan Johnson, Nov 14 2013
STATUS
approved