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A325196 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.

%I A325196 #12 Apr 24 2019 10:11:27
%S A325196 3,4,9,10,12,15,18,20,42,45,50,60,63,70,75,84,90,100,105,126,140,150,
%T A325196 294,315,330,350,420,441,462,490,495,525,550,588,630,660,693,700,735,
%U A325196 770,825,882,924,980,990,1050,1100,1155,1386,1470,1540,1650,2730,3234
%N A325196 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 A325196 The enumeration of these partitions by sum is given by A325191.
%H A325196 Gus Wiseman, <a href="/A325196/a325196.png">Young diagrams for their first 60 terms</a>.
%H A325196 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 A325196 FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000384">St000384: The maximal part of the shifted composition of an integer partition</a>.
%e A325196 The sequence of terms together with their prime indices begins:
%e A325196     3: {2}
%e A325196     4: {1,1}
%e A325196     9: {2,2}
%e A325196    10: {1,3}
%e A325196    12: {1,1,2}
%e A325196    15: {2,3}
%e A325196    18: {1,2,2}
%e A325196    20: {1,1,3}
%e A325196    42: {1,2,4}
%e A325196    45: {2,2,3}
%e A325196    50: {1,3,3}
%e A325196    60: {1,1,2,3}
%e A325196    63: {2,2,4}
%e A325196    70: {1,3,4}
%e A325196    75: {2,3,3}
%e A325196    84: {1,1,2,4}
%e A325196    90: {1,2,2,3}
%e A325196   100: {1,1,3,3}
%e A325196   105: {2,3,4}
%e A325196   126: {1,2,2,4}
%t A325196 primeptn[n_]:=If[n==1,{},Reverse[Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]];
%t A325196 otb[ptn_]:=Min@@MapIndexed[#1+#2[[1]]-1&,Append[ptn,0]];
%t A325196 otbmax[ptn_]:=Max@@MapIndexed[#1+#2[[1]]-1&,Append[ptn,0]];
%t A325196 Select[Range[1000],otbmax[primeptn[#]]-otb[primeptn[#]]==1&]
%Y A325196 Cf. A060687, A065770, A256617, A325166, A325169, A325179, A325181, A325183, A325185, A325188, A325189, A325191, A325195, A325200.
%K A325196 nonn
%O A325196 1,1
%A A325196 _Gus Wiseman_, Apr 11 2019