

A063512


Least number starting a chain of exactly 2n1 consecutive integers that do not have totientinverses.


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
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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..2n2}.


EXAMPLE

n=6: a(6)=865 because it is the first number initiating a chain of exactly 2.61=11 consecutive integers, {865,...,875}, such that each has no totientinverse.


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



