login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A049108 a(n) is the number of iterations of Euler phi function needed to reach 1 starting at n (n is counted). 17
1, 2, 3, 3, 4, 3, 4, 4, 4, 4, 5, 4, 5, 4, 5, 5, 6, 4, 5, 5, 5, 5, 6, 5, 6, 5, 5, 5, 6, 5, 6, 6, 6, 6, 6, 5, 6, 5, 6, 6, 7, 5, 6, 6, 6, 6, 7, 6, 6, 6, 7, 6, 7, 5, 7, 6, 6, 6, 7, 6, 7, 6, 6, 7, 7, 6, 7, 7, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 7, 6, 7, 8, 6, 8, 6, 7, 7, 8, 6, 7, 7, 7, 7, 7, 7, 8, 6, 7, 7, 8, 7, 8, 7, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

R. Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

By the definition of a(n) we have for n >= 2 the recursion a(n) = a(Phi(n)) + 1. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 20 2001

log_3 n << a(n) << log_2 n. - Charles R Greathouse IV, Feb 07 2012

EXAMPLE

If n=164 the trajectory is {164,80,32,16,8,4,2,1}. Its length is 8, thus a(164)=8.

MATHEMATICA

f[n_] := Length[NestWhileList[ EulerPhi, n, # != 1 &]]; Array[f, 105] (* Robert G. Wilson v, Feb 07 2012 *)

PROG

(PARI) a(n)=my(t=1); while(n>1, t++; n=eulerphi(n)); t \\ Charles R Greathouse IV, Feb 07 2012

CROSSREFS

Cf. A000010, A007755. Equals A003434 + 1.

Sequence in context: A085887 A297616 A213251 * A179846 A086925 A088858

Adjacent sequences:  A049105 A049106 A049107 * A049109 A049110 A049111

KEYWORD

nonn,nice,easy,changed

AUTHOR

Labos Elemer

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified May 27 07:54 EDT 2018. Contains 304690 sequences. (Running on oeis4.)