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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*n/8*log(log(n)) < Phi(n) < n, for n > 30. a(30) = 9377213. LINKS Amiram Eldar, Table of n, a(n) for n = 1..52 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 Cf. A000010, A007617, A005277. Sequence in context: A090754 A067764 A193930 * A199317 A205776 A132846 Adjacent sequences:  A063509 A063510 A063511 * A063513 A063514 A063515 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 January 25 19:00 EST 2022. Contains 350572 sequences. (Running on oeis4.)