A049117 - OEIS

%I #22 Oct 15 2013 22:30:26

%S 3,7,19,47,163,487,1307,2879,19683,39367,177147,531441,1594323,

%T 4782969,14348907,43046721,86093443,258280327,688747547,3486784401,

%U 10460353203

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

%C a(21) <= 31381059609 = 3^22. [_Donovan Johnson_, Feb 06 2010]

%C 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

%e The corresponding iterated phi-sequences are:

%e {3, 2, 1},

%e {7, 6, 2, 1},

%e {19, 18, 6, 2, 1},

%e {47, 46, 22, 10, 4, 2, 1},

%e {163, 162, 54, 18, 6, 2, 1},

%e {487, 486, 162, 54, 18, 6, 2, 1}, ...

%t 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 *)

%Y A variant of A227946.

%Y Cf. A000010.

%K nonn,more

%O 0,1

%A _Labos Elemer_

%E More terms from _Jud McCranie_, Jan 14 2000

%E More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Sep 04 2006

%E a(19)-a(20) from _Donovan Johnson_, Feb 06 2010