|
%I #14 Apr 24 2019 10:11:21
%S 0,0,1,1,2,0,3,2,1,1,4,1,5,2,1,3,6,1,7,1,2,3,8,2,2,4,2,2,9,0,10,4,3,5,
%T 2,2,11,6,4,2,12,1,13,3,1,7,14,3,3,1,5,4,15,2,3,2,6,8,16,1,17,9,1,5,4,
%U 2,18,5,7,1,19,3,20,10,1,6,3,3,21,3,3,11
%N Difference between the length of the minimal triangular partition containing and the maximal triangular partition contained in the Young diagram of the integer partition with Heinz number n.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%H FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000384">St000384: The maximal part of the shifted composition of an integer partition</a>
%H FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000783">St000783: The maximal number of occurrences of a colour in a proper colouring of a Ferrers diagram</a>
%e The partition (3,3) has Heinz number 25 and diagram
%e o o o
%e o o o
%e containing maximal triangular partition
%e o o
%e o
%e and contained in minimal triangular partition
%e o o o o
%e o o o
%e o o
%e o
%e so a(25) = 4 - 2 = 2.
%t primeptn[n_]:=If[n==1,{},Reverse[Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]];
%t otb[ptn_]:=Min@@MapIndexed[#1+#2[[1]]-1&,Append[ptn,0]];
%t otbmax[ptn_]:=Max@@MapIndexed[#1+#2[[1]]-1&,Append[ptn,0]];
%t Table[otbmax[primeptn[n]]-otb[primeptn[n]],{n,100}]
%Y Cf. A046660, A065770, A071724, A243055, A325166, A325169, A325178, A325183, A325188, A325189, A325191, A325196, A325197, A325199, A325200.
%K nonn
%O 1,5
%A _Gus Wiseman_, Apr 11 2019
|
