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A063512 Least number starting a chain of exactly 2n-1 consecutive integers that do not have totient inverses. 14
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; text; internal format)
OFFSET
1,1
COMMENTS
(3/8)*n*log(log(n)) < phi(n) < n for n > 30.
LINKS
FORMULA
a(n) = Min{x : invphi(x+j) is empty exactly for j=0..2n-2}.
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.
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}]
CROSSREFS
Sequence in context: A067764 A193930 A367756 * A199317 A205776 A132846
KEYWORD
nonn
AUTHOR
Labos Elemer, Aug 22 2001
EXTENSIONS
Edited and extended by Robert G. Wilson v, May 28 2002 and Jul 11 2002
David Wasserman 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, Oct 20 2011
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)