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A369562
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Smallest positive n-digit number divisible by 7.
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0
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7, 14, 105, 1001, 10003, 100002, 1000006, 10000004, 100000005, 1000000001, 10000000003, 100000000002, 1000000000006, 10000000000004, 100000000000005, 1000000000000001, 10000000000000003, 100000000000000002, 1000000000000000006, 10000000000000000004, 100000000000000000005
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OFFSET
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1,1
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COMMENTS
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The only semiprime terms are a(2) = 14 and a(n) such that (10^(n-1) + 3)/7 is a prime. - Jon E. Schoenfield, Jan 27 2024
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LINKS
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FORMULA
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a(n) = (floor(10^(n-1)/7) + 1)*7.
G.f.: 7*x*(1 - 9*x + 3*x^2 - x^3 - 3*x^4)/((1 - x)*(1 + x)*(1 - 10*x)*(1 - x + x^2)). - Stefano Spezia, Jan 28 2024
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EXAMPLE
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a(3) = 105 = 7*15.
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MATHEMATICA
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a[n_] := 10^(n - 1) + {6, 4, 5, 1, 3, 2}[[Mod[n, 6, 1]]]; Array[a, 30]
(* or *)
LinearRecurrence[{11, -10, -1, 11, -10}, {7, 14, 105, 1001, 10003, 100002}, 30] (* Amiram Eldar, Jan 27 2024 *)
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CROSSREFS
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KEYWORD
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nonn,easy,base
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AUTHOR
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STATUS
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approved
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