

A325610


Adjusted frequency depth of 2^n  1.


4



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, 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, 3, 3, 3, 5, 3, 3, 3, 3, 3, 5, 3, 5, 3, 3, 3, 5, 3, 3, 3
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,4


COMMENTS

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.


LINKS

Table of n, a(n) for n=1..87.


MATHEMATICA

fdadj[ptn_List]:=If[ptn=={}, 0, Length[NestWhileList[Sort[Length/@Split[#1]]&, ptn, Length[#1]>1&]]];
Table[fdadj[2^n1], {n, 100}]


CROSSREFS

Cf. A001222, A001221, A056239, A071625, A112798, A323014, A325280.
Mersenne numbers: A046051, A046800, A059305, A325611, A325612, A325625.
Sequence in context: A165595 A213181 A301848 * A278536 A143825 A290478
Adjacent sequences: A325607 A325608 A325609 * A325611 A325612 A325613


KEYWORD

nonn


AUTHOR

Gus Wiseman, May 12 2019


STATUS

approved



