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A325197 Heinz numbers of integer partitions such that the difference between the length of the minimal triangular partition containing and the maximal triangular partition contained in the Young diagram is 2.

%I A325197 #14 Apr 24 2019 10:11:34
%S A325197 5,8,14,21,24,25,27,28,35,36,40,54,56,66,98,99,110,120,125,132,135,
%T A325197 147,154,165,168,175,180,189,196,198,200,220,225,231,245,250,252,264,
%U A325197 270,275,280,297,300,308,375,378,385,390,392,396,440,450,500,546,585,594
%N A325197 Heinz numbers of integer partitions such that the difference between the length of the minimal triangular partition containing and the maximal triangular partition contained in the Young diagram is 2.
%C A325197 The enumeration of these partitions by sum is given by A325199.
%H A325197 FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000384">St000384: The maximal part of the shifted composition of an integer partition</a>
%H A325197 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>
%H A325197 Gus Wiseman, <a href="/A325197/a325197.png">Young diagrams for their first 60 terms</a>
%e A325197 The sequence of terms together with their prime indices begins:
%e A325197     5: {3}
%e A325197     8: {1,1,1}
%e A325197    14: {1,4}
%e A325197    21: {2,4}
%e A325197    24: {1,1,1,2}
%e A325197    25: {3,3}
%e A325197    27: {2,2,2}
%e A325197    28: {1,1,4}
%e A325197    35: {3,4}
%e A325197    36: {1,1,2,2}
%e A325197    40: {1,1,1,3}
%e A325197    54: {1,2,2,2}
%e A325197    56: {1,1,1,4}
%e A325197    66: {1,2,5}
%e A325197    98: {1,4,4}
%e A325197    99: {2,2,5}
%e A325197   110: {1,3,5}
%e A325197   120: {1,1,1,2,3}
%e A325197   125: {3,3,3}
%e A325197   132: {1,1,2,5}
%t A325197 primeptn[n_]:=If[n==1,{},Reverse[Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]];
%t A325197 otb[ptn_]:=Min@@MapIndexed[#1+#2[[1]]-1&,Append[ptn,0]];
%t A325197 otbmax[ptn_]:=Max@@MapIndexed[#1+#2[[1]]-1&,Append[ptn,0]];
%t A325197 Select[Range[1000],otbmax[primeptn[#]]-otb[primeptn[#]]==2&]
%Y A325197 Cf. A195086, A065770, A325166, A325168, A325169, A325170, A325180, A325182, A325188, A325189, A325195, A325196, A325198, A325199, A325200.
%K A325197 nonn
%O A325197 1,1
%A A325197 _Gus Wiseman_, Apr 11 2019