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A053050
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Smallest integer m such that sum_(k=1 to m) prime(k) is divisible by n.
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2
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1, 1, 10, 5, 2, 57, 5, 11, 20, 3, 8, 97, 49, 5, 57, 11, 4, 113, 23, 9, 40, 17, 23, 99, 9, 49, 26, 5, 7, 57, 39, 11, 76, 13, 180, 119, 29, 23, 119, 11, 6, 305, 10, 17, 242, 23, 39, 119, 40, 9, 179, 49, 25, 187, 17, 115, 70, 7, 30, 103, 151, 39, 40, 171, 131, 175, 38, 37, 52, 209, 19
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| It follows from a theorem of Daniel Shiu that m always exists. See A111287 for details. - N. J. A. Sloane (njas(AT)research.att.com), Nov 05 2005
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REFERENCES
| D. K. L. Shiu, Strings of congruent primes, J. London Math. Soc. 61 (2000), 359-373; MR 2001f:11155.
Felice Russo, A set of new Smarandache functions, sequences and conjectures in number theory, American Research Press 2000
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
M. L. Perez et al., eds., Smarandache Notions Journal
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MAPLE
| read transforms; M:=1000; p0:=[seq(ithprime(i), i=1..M)]; q0:=PSUM(p0); w:=[]; for n from 1 to M do p:=n; hit := 0; for i from 1 to M do if q0[i] mod p = 0 then w:=[op(w), i]; hit:=1; break; fi; od: if hit = 0 then break; fi; od: w;
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MATHEMATICA
| Transpose[With[{aprs=Thread[{Range[500], Accumulate[Prime[Range[ 500]]]}]}, Flatten[Table[Select[aprs, Divisible[Last[#], n]&, 1], {n, 80}], 1]]][[1]] (* From Harvey P. Dale, Dec 14 2011 *)
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PROG
| (Haskell)
import Data.List (findIndex)
import Data.Maybe (fromJust)
a053050 n = (fromJust $ findIndex ((== 0) . (`mod` n)) a007504_list) + 1
-- Reinhard Zumkeller, Feb 10 2012
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CROSSREFS
| Cf. A007504, A111287, A002034, A011772.
Sequence in context: A038306 A117256 A050020 * A033330 A102584 A134167
Adjacent sequences: A053047 A053048 A053049 * A053051 A053052 A053053
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KEYWORD
| easy,nice,nonn,changed
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AUTHOR
| Felice Russo (frusso(AT)micron.com), Feb 25 2000
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EXTENSIONS
| More terms from N. J. A. Sloane (njas(AT)research.att.com), Nov 05 2005
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