This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A053048 #17 Aug 17 2024 09:01:39
%S A053048 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,
%T A053048 57,57,60,63,66,69,74,77,82,85,87,89,91,93,98,103,105,107,112,114,119,
%U A053048 124,128,130,135,139,143,147,148,153,157,158,162,166,170,174,178,179
%N 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!.
%H A053048 Amiram Eldar, <a href="/A053048/b053048.txt">Table of n, a(n) for n = 1..10000</a>
%F A053048 a(n) = log_2(A053047(n)). - _Amiram Eldar_, Aug 17 2024
%e A053048 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.
%t A053048 a[n_] := Max@ IntegerExponent[ FixedPointList[ EulerPhi, n!], 2]; Array[a, 63] (* _Giovanni Resta_, May 30 2018 *)
%Y A053048 Cf. A000010, A000142, A048855, A053039, A053047.
%K A053048 nonn
%O A053048 1,4
%A A053048 _Labos Elemer_, Feb 25 2000