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

Author

Labos Elemer, Aug 22 2001

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..52

Crossrefs

Cf. A000010, A007617, A005277.

Programs

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}]

Formula

a(n) = Min{x : invphi(x+j) is empty exactly for j=0..2n-2}.

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