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Smallest m such that the number of iterations of "take odd part of phi" to reach 1 from m (A227944) is n.
4

%I #33 Nov 11 2013 10:29:40

%S 1,2,7,19,47,163,487,1307,2879,19683,39367,177147,531441,1594323,

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

%U 10460353203

%N Smallest m such that the number of iterations of "take odd part of phi" to reach 1 from m (A227944) is n.

%C The odd part of a number is its largest odd divisor (A000265), phi is Euler's totient function (A000010). - _Alonso del Arte_, Oct 13 2013

%F a(n) = smallest m such that A227944(m)=n.

%e a(1) = 2 because just one step is needed to reach 1 from 2, since phi(2) = 1. The numbers 3, 4, 5 and 6 also take one step.

%e a(2) = 7 because two steps are needed to reach 1 from 7: phi(7) = 6, the odd part of which is 3, and phi(3) = 2, the odd part of which is 1. The numbers from 8 to 18 take one or two steps to reach 1.

%e a(3) = 19 because three steps are needed to reach 1 from 19: phi(19) = 18, the odd part of which is 9, and phi(9) = 6, the odd part of which is 3, and phi(3) = 2, the odd part of which is 1.

%o (Haskell)

%o import Data.List (elemIndex); import Data.Maybe (fromJust)

%o a227946 = (+ 1) . fromJust . (`elemIndex` a227944_list)

%o -- _Reinhard Zumkeller_, Nov 10 2013

%Y A variant of A049117. - _R. J. Mathar_, Oct 06 2013

%Y Cf. A007755, A053575, A000010.

%K nonn,more

%O 0,2

%A _Max Alekseyev_, Oct 03 2013

%E a(15) through a(21) copied over from A049117 by _Max Alekseyev_, Oct 13 2013