A049117 Smallest number which when Euler phi function is repeatedly applied have not reached a power of 2 in n steps.

3, 7, 19, 47, 163, 487, 1307, 2879, 19683, 39367, 177147, 531441, 1594323, 4782969, 14348907, 43046721, 86093443, 258280327, 688747547, 3486784401, 10460353203

Offset: 0

Author

Labos Elemer

Keywords

• nonn
• more

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

Examples

			The corresponding iterated phi-sequences 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}, ...
		

Crossrefs

A variant of A227946.

Cf. A000010.

Programs

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 *)

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