%I #14 Apr 24 2019 10:11:34
%S 5,8,14,21,24,25,27,28,35,36,40,54,56,66,98,99,110,120,125,132,135,
%T 147,154,165,168,175,180,189,196,198,200,220,225,231,245,250,252,264,
%U 270,275,280,297,300,308,375,378,385,390,392,396,440,450,500,546,585,594
%N 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 The enumeration of these partitions by sum is given by A325199.
%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>
%H Gus Wiseman, <a href="/A325197/a325197.png">Young diagrams for their first 60 terms</a>
%e The sequence of terms together with their prime indices begins:
%e 5: {3}
%e 8: {1,1,1}
%e 14: {1,4}
%e 21: {2,4}
%e 24: {1,1,1,2}
%e 25: {3,3}
%e 27: {2,2,2}
%e 28: {1,1,4}
%e 35: {3,4}
%e 36: {1,1,2,2}
%e 40: {1,1,1,3}
%e 54: {1,2,2,2}
%e 56: {1,1,1,4}
%e 66: {1,2,5}
%e 98: {1,4,4}
%e 99: {2,2,5}
%e 110: {1,3,5}
%e 120: {1,1,1,2,3}
%e 125: {3,3,3}
%e 132: {1,1,2,5}
%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 Select[Range[1000],otbmax[primeptn[#]]-otb[primeptn[#]]==2&]
%Y Cf. A195086, A065770, A325166, A325168, A325169, A325170, A325180, A325182, A325188, A325189, A325195, A325196, A325198, A325199, A325200.
%K nonn
%O 1,1
%A _Gus Wiseman_, Apr 11 2019
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