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A063512
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Least number starting a chain of exactly 2n-1 consecutive integers that do not have totient inverses.
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14
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3, 13, 73, 401, 241, 865, 8405, 4033, 10567, 14261, 35171, 64521, 112691, 134641, 256831, 159121, 1214533, 597081, 2277139, 1039681, 5972401, 2307317, 12033793, 9403681, 5313463, 23777761, 84502091, 19773769, 159227791, 9377213, 146793539, 114748705, 245856241
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OFFSET
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1,1
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COMMENTS
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(3/8)*n*log(log(n)) < phi(n) < n for n > 30.
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LINKS
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FORMULA
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a(n) = Min{x : invphi(x+j) is empty exactly for j=0..2n-2}.
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EXAMPLE
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n=6: a(6)=865 because it is the first number initiating a chain of exactly 2*6-1=11 consecutive integers, {865,...,875}, such that each has no totient inverse.
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MATHEMATICA
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a = Table[0, {5*10^7}]; Do[b = EulerPhi[n]/2; If[b < 5*10^7 + 1, a[[b]]++ ], {n, 3, 5*10^8}]; (* used to find a(7) *) Do[ If[ a[[n]] == a[[n + 1]] == a[[n + 2]] == a[[n + 3]] == a[[n + 4]] == a[[n + 5]] == a[[n + 6]] == 0, Print[2n - 1]], {n, 1, 5*10^7 -6}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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David Wasserman pointed out that a(21) was incorrect and supplied a better description on Jul 10 2002
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STATUS
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approved
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