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Search: id:A112272
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| A112272 |
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One seventh of the sum of the first n primes, when an integer. |
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+0
2
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| 4, 11, 34, 113, 284, 441, 634, 731, 943, 1226, 1657, 2343, 2469, 3767, 3931, 4271, 4712, 5759, 5963, 7154, 8221, 8467, 8971, 9362, 9763, 12655, 13279, 13595, 13915, 15941, 17560, 19641, 21261, 21675, 22091, 22937, 23363, 23793, 24671, 26702
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(1) = 4 and a(6) = 441 are perfect squares. What is the next term in this subsequence? Answer from Stefan Steinerberger: a(103)=315844=562^2.
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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)/7 iff 7 | A007504(k)}. {a(n)} = {(p_1 + p_2 + ... + p_k)/7 iff the sum is an integer}.
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EXAMPLE
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a(1) = 4 = (2+3+5+7+11)/7 = A007504(5)/7 = 28/7.
a(2) = 11 = (2+3+5+7+11+13+17+19)/5 = A007504(8)/7 = 77/7.
a(3) = 34 = A007504(13)/5 = 238/7.
a(4) = 113 = A007504(22)/5 = 791/7.
a(5) = 284 = A007504(33)/5 = 1988/7.
a(6) = 441 = A007504(40)/5 = 3087/7.
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MATHEMATICA
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s = 0; lst = {}; Do[s = s + Prime[n]; If[Mod[s, 7] == 0, AppendTo[lst, s/7]], {n, 270}]; lst (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A000040, A007504, A112040.
Sequence in context: A027045 A006765 A151272 this_sequence A149234 A149235 A149236
Adjacent sequences: A112269 A112270 A112271 this_sequence A112273 A112274 A112275
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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 02 2005
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