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%I #12 Apr 24 2019 10:11:27
%S 3,4,9,10,12,15,18,20,42,45,50,60,63,70,75,84,90,100,105,126,140,150,
%T 294,315,330,350,420,441,462,490,495,525,550,588,630,660,693,700,735,
%U 770,825,882,924,980,990,1050,1100,1155,1386,1470,1540,1650,2730,3234
%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 1.
%C The enumeration of these partitions by sum is given by A325191.
%H Gus Wiseman, <a href="/A325196/a325196.png">Young diagrams for their first 60 terms</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 FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000384">St000384: The maximal part of the shifted composition of an integer partition</a>.
%e The sequence of terms together with their prime indices begins:
%e 3: {2}
%e 4: {1,1}
%e 9: {2,2}
%e 10: {1,3}
%e 12: {1,1,2}
%e 15: {2,3}
%e 18: {1,2,2}
%e 20: {1,1,3}
%e 42: {1,2,4}
%e 45: {2,2,3}
%e 50: {1,3,3}
%e 60: {1,1,2,3}
%e 63: {2,2,4}
%e 70: {1,3,4}
%e 75: {2,3,3}
%e 84: {1,1,2,4}
%e 90: {1,2,2,3}
%e 100: {1,1,3,3}
%e 105: {2,3,4}
%e 126: {1,2,2,4}
%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[#]]==1&]
%Y Cf. A060687, A065770, A256617, A325166, A325169, A325179, A325181, A325183, A325185, A325188, A325189, A325191, A325195, A325200.
%K nonn
%O 1,1
%A _Gus Wiseman_, Apr 11 2019
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