A053475 1 + the number of iterations of A051953 (Euler-cototient) function needed to reach 0, starting at n.

2, 3, 3, 4, 3, 5, 3, 5, 4, 6, 3, 6, 3, 6, 4, 6, 3, 7, 3, 7, 5, 7, 3, 7, 4, 7, 5, 7, 3, 8, 3, 7, 4, 8, 4, 8, 3, 8, 5, 8, 3, 9, 3, 8, 6, 8, 3, 8, 4, 9, 4, 8, 3, 9, 5, 8, 6, 9, 3, 9, 3, 8, 6, 8, 4, 9, 3, 9, 5, 9, 3, 9, 3, 9, 5, 9, 4, 10, 3, 9, 6, 10, 3, 10, 6, 9, 4, 9, 3, 10, 4, 9, 5, 9, 4, 9, 3, 9, 6, 10, 3, 10

Offset

1,1

Comments

Analogous sequences of iteration-lengths for A000005 or A000010 are A036459 and A049108 resp. The length values of 3 occur if the initial value is prime resulting in {p,1,0} iterations.

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Formula

a(n) = A076640(n) + 1. - Michael De Vlieger, Jul 04 2016

Example

Starting with n=18, the iterations of A051953 are as follows: {18,12,8,4,2,1,0}. The length of this sequence is 7, so a(18) = 7. The function is applied a(n)-1 times.

Mathematica

Table[Length@ NestWhileList[# - EulerPhi@ # &, n, # > 0 &], {n, 84}] (* Michael De Vlieger, Jul 04 2016 *)

Crossrefs

Cf. A000005, A000010, A051953, A036459, A049108, A076640.

Sequence in context: A088858 A113312 A334954 * A140605 A350064 A351085

Adjacent sequences: A053472 A053473 A053474 * A053476 A053477 A053478

Keyword

nonn

Author

Labos Elemer, Jan 14 2000

Status

approved