A053048 a(n) is the number of terminal iterations applied to powers of 2 arising in the iterations of the Euler phi function with initial value n!.

0, 1, 1, 3, 5, 6, 7, 10, 10, 13, 16, 18, 20, 22, 24, 28, 32, 33, 34, 38, 39, 43, 47, 50, 54, 57, 57, 60, 63, 66, 69, 74, 77, 82, 85, 87, 89, 91, 93, 98, 103, 105, 107, 112, 114, 119, 124, 128, 130, 135, 139, 143, 147, 148, 153, 157, 158, 162, 166, 170, 174, 178, 179

Offset

1,4

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = log_2(A053047(n)). - Amiram Eldar, Aug 17 2024

Example

For n = 10, the initial value is 10! = 3628800 and the iteration chain is {3628800, 829440, 221184, 73728, 24576, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1}. The first power of 2 is 8192, after which phi is applied 13 additional times to reach the stationary value 1.

Mathematica

a[n_] := Max@ IntegerExponent[ FixedPointList[ EulerPhi, n!], 2]; Array[a, 63] (* Giovanni Resta, May 30 2018 *)

Crossrefs

Cf. A000010, A000142, A048855, A053039, A053047.

Sequence in context: A124194 A359506 A055597 * A154663 A028983 A232682

Adjacent sequences: A053045 A053046 A053047 * A053049 A053050 A053051

Keyword

nonn

Author

Labos Elemer, Feb 25 2000

Status

approved