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%I #5 May 13 2019 01:09:54
%S 0,1,1,3,1,4,1,3,3,3,3,5,1,3,3,3,1,5,1,5,5,3,3,5,3,3,3,3,3,5,1,3,3,3,
%T 3,5,3,3,3,5,3,5,3,3,3,3,3,5,3,3,3,3,3,5,3,3,3,3,3,5,1,3,5,3,3,5,3,3,
%U 3,3,3,5,3,3,3,3,3,5,3,5,3,3,3,5,3,3,3
%N Adjusted frequency depth of 2^n - 1.
%C The adjusted frequency depth of a positive integer n is 0 if n = 1, and otherwise it is 1 plus the number of times one must apply A181819 to reach a prime number, where A181819(k = p^i*...*q^j) = prime(i)*...*prime(j) = product of primes indexed by the prime exponents of k. For example, 180 has adjusted frequency depth 5 because we have: 180 -> 18 -> 6 -> 4 -> 3.
%t fdadj[ptn_List]:=If[ptn=={},0,Length[NestWhileList[Sort[Length/@Split[#1]]&,ptn,Length[#1]>1&]]];
%t Table[fdadj[2^n-1],{n,100}]
%Y Cf. A001222, A001221, A056239, A071625, A112798, A323014, A325280.
%Y Mersenne numbers: A046051, A046800, A059305, A325611, A325612, A325625.
%K nonn
%O 1,4
%A _Gus Wiseman_, May 12 2019
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