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Search: id:A112270
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| A112270 |
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One third of the sum of the first n primes, when an integer. |
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+0
2
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| 43, 127, 167, 213, 321, 387, 457, 531, 617, 709, 809, 1029, 1149, 1277, 1409, 1863, 2027, 2290, 3397, 3629, 4113, 4367, 4629, 4899, 5179, 5467, 5761, 6063, 6371, 7516, 7864, 8600, 8980, 9368, 10168, 10578, 11856, 12296, 12746, 13204, 13674, 14156
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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Bach, E. and Shallit, J. Sect. 2.7 in Algorithmic Number Theory, Vol. 1: Efficient Algorithms. Cambridge, MA: MIT Press, 1996.
Moser, L. "Notes on Number Theory III. On the Sum of Consecutive Primes." Can. Math. Bull. 6, 159-161, 1963.
H. L. Nelson, "Prime Sums", J. Rec. Math., 14 (1981), 205-206.
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LINKS
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Eric Weisstein's World of Mathematics, Prime Sums.
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FORMULA
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{a(n)} = {A007504(k)/3 iff 3 | A007504(k)}. {a(n)} = {(p_1 + p_2 + ... + p_k)/3 iff the sum is an integer}. It is necessary but not sufficient for k to be even.
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EXAMPLE
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a(1) = 43 = (2+3+5+7+11+13+17+19+23+29)/3 = A007504(10)/3 = 129/3.
a(2) = 127 = A007504(16)/3 = 381/3.
a(3) = 167 = A007504(18)/3 = 501/3.
a(4) = 213 = A007504(20)/3 = 639/3.
a(5) = 321 = A007504(24)/3 = 963/3.
a(6) = 387 = A007504(26)/3 = 1161/3.
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MATHEMATICA
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s = 0; lst = {}; Do[s = s + Prime[n]; If[Mod[s, 3] == 0, AppendTo[lst, s/3]], {n, 130}]; lst (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A000040, A007504, A112040.
Sequence in context: A029816 A044294 A044675 this_sequence A124826 A136069 A140028
Adjacent sequences: A112267 A112268 A112269 this_sequence A112271 A112272 A112273
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Nov 30 2005
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Nov 30 2005
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