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A175203
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Numbers k that divide 10^(k+1)-1 .
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1
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1, 3, 9, 11, 33, 77, 99, 143, 303, 369, 407, 707, 959, 1001, 1111, 2439, 2703, 2717, 2849, 3107, 3399, 3519, 4059, 4277, 5151, 5291, 6083, 6439, 6479, 8687, 9191, 9799, 9999, 10403, 10439, 10619, 11951, 12089, 13727, 13919, 16211, 18699, 22119, 24849
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OFFSET
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1,2
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REFERENCES
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J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 303, p. 76, Ellipses, Paris 2008.
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LINKS
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EXAMPLE
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3 divides 10^4 - 1 = 3^2 * 11 * 101.
9 divides 10^10 - 1 = 3^2 * 11 * 41 * 271 * 9091.
11 divides 10^12 - 1 = 3^3 * 7 * 11 * 13 * 37 * 101 * 9901.
33 divides 10^34 - 1 = 3^2 * 11 * 103 * 4013 * 2071723 * 5363222357 * 21993833369.
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MAPLE
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with(numtheory):for n from 1 to 50000 do: x:= 10^(n+1) - 1: y:=irem(x, n): if y=0 then print (n):else fi:od:
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MATHEMATICA
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Select[Flatten[10*#-{9, 7, 3, 1} & /@ Range@10000],
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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