A287415 a(0) = 0; a(1) = 1; a(n) = n - a(phi(a(n-1))), where phi() is the Euler totient function (A000010).

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

Offset

0,4

Comments

A variation on Hofstadter's G-sequence.

Links

Table of n, a(n) for n=0..79.

Ilya Gutkovskiy, Extended graphical example

Index entries for Hofstadter-type sequences

Formula

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

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

Mathematica

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

Crossrefs

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

Sequence in context: A135681 A135680 A135682 * A352612 A083245 A111610

Adjacent sequences: A287412 A287413 A287414 * A287416 A287417 A287418

Keyword

nonn

Author

Ilya Gutkovskiy, May 24 2017

Status

approved