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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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5
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 3*n/8*ln(ln(n)) < Phi(n) < n, for n > 30.
a(30) = 9377213.
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FORMULA
| a(n)=Min{x : invphi(x+j) is empty exactly for j=0..2n-2}
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EXAMPLE
| 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
| 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
| Cf. A000010, A007617, A005277.
Sequence in context: A090754 A067764 A193930 * A199317 A205776 A132846
Adjacent sequences: A063509 A063510 A063511 * A063513 A063514 A063515
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Aug 22 2001
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EXTENSIONS
| Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), May 28 2002 and Jul 11 2002
David Wasserman (dwasserm(AT)earthlink.com) pointed out that a(21) was incorrect and supplied a better description on Jul 10 2002
a(29) and a(31)-a(33) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Oct 20 2011
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