A063512 Least number starting a chain of exactly 2n-1 consecutive integers that do not have totient inverses.

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

Offset

1,1

Comments

(3/8)*n*log(log(n)) < phi(n) < n for n > 30.

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: A067764 A193930 A367756 * 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