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A258663
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Numbers n such that 9n-1 is prime.
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3
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2, 6, 8, 10, 12, 20, 22, 26, 28, 30, 40, 48, 50, 52, 56, 58, 62, 66, 72, 76, 78, 80, 86, 90, 92, 96, 98, 106, 108, 118, 122, 128, 132, 136, 140, 142, 152, 160, 166, 168, 176, 178, 180, 182, 190, 208, 210, 212, 220, 222, 230, 232, 238, 246, 252, 260
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OFFSET
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1,1
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COMMENTS
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It is my conjecture that the integer formed by the repeating digits in the decimal fraction a(n)/(a(n)*9-1) is the smallest integer such that rotating the digits to the left produces a number which is ((a(n)+1)/a(n)) times larger.
Example: a(n) = 2: 2/17 = 0.1176470588235294... repeating with a cycle of 16.
1176470588235294 x (3/2) = 1764705882352941, which is 1176470588235294 rotated to the left.
An additional conjecture is that the values x in this sequence are the only values where rotating an integer one to the left produces a value (x+1)/x times as large. For example, the conjecture is that there are integers i that when rotated one to the left produce the value 3i/2, 7i/6 and 9i/8, but none that produce the value 2i/1, 4i/3, 5i/4, 6i/5 or 8i/7.
All of the terms in this sequence are even numbers that do not end with 4. (9n-1 is even for odd n and ends with 5 when the final digit of n = 4.) - Doug Bell, Jun 25 2015
The second conjecture is false. For example, 225806451612903*(8/7) = 258064516129032, or 45 * (6/5) = 54 or 230769*(4/3)=307692. - Giovanni Resta, Jul 28 2015
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LINKS
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FORMULA
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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