cp's OEIS Frontend

A325169 Origin-to-boundary graph-distance of the Young diagram of the integer partition with Heinz number n.

%I A325169 #16 Jan 08 2021 21:17:10
%S A325169 0,1,1,1,1,2,1,1,2,2,1,2,1,2,2,1,1,2,1,2,2,2,1,2,2,2,2,2,1,3,1,1,2,2,
%T A325169 2,2,1,2,2,2,1,3,1,2,3,2,1,2,2,3,2,2,1,2,2,2,2,2,1,3,1,2,3,1,2,3,1,2,
%U A325169 2,3,1,2,1,2,3,2,2,3,1,2,2,2,1,3,2,2,2
%N A325169 Origin-to-boundary graph-distance of the Young diagram of the integer partition with Heinz number n.
%C A325169 The origin-to-boundary graph-distance of a Young diagram is the minimum number of unit steps left or down from the upper-left square to a nonsquare in the lower-right quadrant. It is also the side-length of the minimum triangular partition contained inside the diagram.
%C A325169 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%H A325169 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>
%F A325169 A257990(n) <= a(n) <= 2 * A257990(n).
%t A325169 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A325169 otb[ptn_]:=Min@@MapIndexed[#1+#2[[1]]-1&,Append[ptn,0]];
%t A325169 Table[otb[Reverse[primeMS[n]]],{n,100}]
%Y A325169 Cf. A001221, A001222, A056239, A061395, A065770, A112798, A115994, A174090, A257990, A297113, A325166, A325167, A325170.
%K A325169 nonn
%O A325169 1,6
%A A325169 _Gus Wiseman_, Apr 05 2019