OFFSET
0,3
COMMENTS
The adjusted frequency depth of an integer partition is 0 if the partition is empty, and otherwise it is one plus the number of times one must take the multiset of multiplicities to reach a singleton. For example, the partition (32211) has adjusted frequency depth 5 because we have: (32211) -> (221) -> (21) -> (11) -> (2).
FORMULA
a(0) = 0; a(1) = 1; a(n > 1) = A225486(n).
MATHEMATICA
fdadj[ptn_List]:=If[ptn=={}, 0, Length[NestWhileList[Sort[Length/@Split[#]]&, ptn, Length[#]>1&]]];
Table[Max@@fdadj/@IntegerPartitions[n], {n, 0, 30}]
CROSSREFS
Cf. A011784, A032741, A127002, A181819, A225486, A275870, A323014, A323023, A325245, A325254, A325258, A325278, A325282, A325283.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 18 2019
STATUS
approved