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Search: id:A112271
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| A112271 |
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One fifth of the sum of the first n primes, when an integer. |
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+0
2
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| 1, 2, 20, 32, 88, 212, 296, 344, 1070, 1166, 1374, 1655, 2248, 2698, 3368, 3730, 3916, 4936, 5160, 5388, 6725, 6983, 8788, 11338, 12382, 12923, 13480, 15026, 16244, 17717, 19033, 19481, 19937, 21108, 24584, 29191, 30345, 33008, 33921, 34850
(list; graph; listen)
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OFFSET
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1,2
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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)/5 iff 5 | A007504(k)}. {a(n)} = {(p_1 + p_2 + ... + p_k)/5 iff the sum is an integer}. It is sufficient that A007504(k) == 0 (mod 10), but not necessary (the last five consecutive primes ending in 1 can give a solution). It is necessary that k = 2 or k is odd.
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EXAMPLE
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a(1) = 1 = (2+3)/5 = A007504(2)/5 = 5/5.
a(2) = 2 = (2+3+5)/5 = A007504(3)/5 = 10/5.
a(3) = 20 = (2+3+5+7+11+13+17+19+23)/5 = A007504(9)/5 = 100/5.
a(4) = 32 = (2+3+5+7+11+13+17+19+23+29+31)/5 = A007504(11)/5 = 160/5.
a(5) = 88 = A007504(17)/5 = 440/5.
a(6) = 212 = A007504(25)/5 = 1060/5.
a(7) = 296 = A007504(29)/5 = 1480/5.
a(8) = 344 = A007504(31)/5 = 1720/5.
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MATHEMATICA
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s = 0; lst = {}; Do[s = s + Prime[n]; If[Mod[s, 5] == 0, AppendTo[lst, s/5]], {n, 250}]; lst (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A000040, A007504, A111319, A112040.
Sequence in context: A078460 A059208 A061471 this_sequence A103076 A062133 A050684
Adjacent sequences: A112268 A112269 A112270 this_sequence A112272 A112273 A112274
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 30 2005
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EXTENSIONS
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More terms from Stefan Steinerberger (hansibal(AT)hotmail.com) and Robert G. Wilson v (rgwv(at)rgwv.com), Dec 04 2005
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