

A049117


Smallest number which when Euler phi function is repeatedly applied have not reached a power of 2 in n steps.


3



3, 7, 19, 47, 163, 487, 1307, 2879, 19683, 39367, 177147, 531441, 1594323, 4782969, 14348907, 43046721, 86093443, 258280327, 688747547, 3486784401, 10460353203
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

a(21) <= 31381059609 = 3^22. [Donovan Johnson, Feb 06 2010]
Note that all terms so far are primes or powers of 3. Is it true that all terms have this form?  T. D. Noe, Oct 07 2013


LINKS

Table of n, a(n) for n=0..20.


EXAMPLE

The corresponding iterated phisequences are:
{3, 2, 1},
{7, 6, 2, 1},
{19, 18, 6, 2, 1},
{47, 46, 22, 10, 4, 2, 1},
{163, 162, 54, 18, 6, 2, 1},
{487, 486, 162, 54, 18, 6, 2, 1}, ...


MATHEMATICA

a[n_] := Module[{i = 1}, While[IntegerQ[Log[2, Nest[EulerPhi, i, n]]], i++ ]; i]; (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Sep 04 2006 *)


CROSSREFS

A variant of A227946.
Cf. A000010.
Sequence in context: A181360 A001372 A179467 * A146810 A246493 A293733
Adjacent sequences: A049114 A049115 A049116 * A049118 A049119 A049120


KEYWORD

nonn,more


AUTHOR

Labos Elemer


EXTENSIONS

More terms from Jud McCranie, Jan 14 2000
More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Sep 04 2006
a(19)a(20) from Donovan Johnson, Feb 06 2010


STATUS

approved



