A287415 - OEIS

%I #14 May 26 2017 16:44:48

%S 0,1,1,2,3,4,5,4,7,4,9,6,11,4,13,4,15,10,15,12,17,6,21,12,21,14,21,16,

%T 21,18,25,14,27,18,29,14,31,12,35,18,35,20,35,22,35,24,39,26,37,18,45,

%U 30,45,32,39,34,41,22,49,24,53,16,55,28,53,20,59,18,63,38,55,36,61,20,67,16,69,42,67,20

%N a(0) = 0; a(1) = 1; a(n) = n - a(phi(a(n-1))), where phi() is the Euler totient function (A000010).

%C A variation on Hofstadter's G-sequence.

%H Ilya Gutkovskiy, <a href="/A287415/a287415.pdf">Extended graphical example</a>

%H <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>

%F a(n) = n - a(a(n-1)*Product_{p|a(n-1), p prime} (1 - 1/p)) for n > 3.

%F a(n) = n - a(a(n-1)-1) for a(n-1) is a prime.

%t a[0] = 0; a[n_] := a[n] = n - a[EulerPhi[a[n - 1]]]; Array[a, 80, 0]

%Y Cf. A000010, A005206, A005374, A135528 (parity of a(n)).

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, May 24 2017